## Short bibliography:

- Research Engineer in the Department of Prof. B. FRAEIJS DE VEUBEKE (1966-1968), (Laboratory of Aerospace Techniques L.T.A.S.), University of LIEGE.
- Assistant of Prof. Ch. MASSONNET (1968-1972), Department of Strength of Materials and Stability of Constructions, University of Liege, Belgium.
- Assistant Professor in the same department (1972-1976).
- Lecturer in the same Department (1978).
- Associate Professor, University of Kinshasa, Zaire (1982-1986).
- "Agrégé de Faculté" (1984-1991), Department of Mechanics of Materials, Stability of Constructions and Mechanics of Structures, Univ. of LIEGE.
- Associate Professor, University of Liege, (chargé de cours, 1984-1991). Depart. of Strength of Materials and Stability of Constructions, University of Liege.
- Professor and Head of the Division LTAS-Fracture Mechanics of Solids (1991- 2006).

## Research

**Rearch domain:**Aerospace

**Rearch interests:**

- Computational Solid MechanicsÂ
- Non-linear Behaviour of SolidsÂ
- Limit State Calculations
- Advanced Solid Mechanics
- Optimisation of Structures
- Structural Analysis
- Fracture Mechanics

## Publications

**In Vietnamese:**

A. Books and Courses

1. "Non-Linear Behaviour of Materials", ( in French) 140 pages, Department of Mechanics of Materials, Stability of Constructions and Mechanics of Structures, University of Liège, (1980).

2. "Applied Static" (in French) - Edition PUZ, Kinshasa, Zaire (1983), 220 pages

3. "Elements of Elasticity" (in French) - Edition PUZ, Kinshasa, Zaire (1983), 120 pages

4. "Strength of Materials" (in French) Tome I, Department of Constructions, Polytechnic Faculty, 170 pages, 1983.

5. "Strength of Materials" (in French) Tome II, Department of Constructions, Polytechnic Faculty, 185 pages, 1983;

6. Applications of the mathematical programming method to structural analysis and design, Engineering Structures, Butterworth, vol. 6, n° 1, January 1984.

7. "On the Plasticity theory and the plastic limit calculations of Structures" (in French), Publication n° 98, Faculty of Applied Sciences, University of Liège (1985), 480 pages.

8. "A course of Elasticity" (in French), Division of "Numerical Modeling in Mechanics and Structures", Department of Mechanics, Technology University of Compiègne, France (1986), 204 pages.

9. "Complements of Mechanics of Solids: plasticity, viscoelasticity,

Fracture Mechanics" (in French), Lecture edited by the " Laboratoire de Mécanique des Matériaux et de Stabilité des Constructions " University of Liège, (1989), 340 pages.

10. "Fracture Mechanics: Numerical approaches" (in French), edited by SAMTECH (1989), 250 pages.

11. "Introduction to Boundary Element Method". A course in French, LTAS_fracture Mechanics, 1990, 120 pages.

12. "A course of Fracture Mechanics" (in French), edited by LTAS-Mécanique de la Rupture des Solides, University of Liège, 1990, 350 pages.

13."Variational and Computational Plastic Limit and Shakedown Analysis" Theory and exercises, to be published by BIRKHAUSER VERLAG, AG, Basel, 500 pages. (To be appeared).

14."Introduction to Solid Mechanics", In French and in Vietnamese, edited by Polytechnic University of Ho Chi Minh City, Vietnam, May 1991, 250 pages.

15. "Advanced fracture mechanics", syllabus in French used during stay I in University of Marseille II (UNIMECA), 1996, 26 pages

16. "Fracture mechanics and finite element method", syllabus in French used during stay I in University of Marseille II (UNIMECA), 1996, 30 pages.

17. "Introduction to the boundary element method", syllabus in French used during stay I in University of Marseille II (UNIMECA), 1996, 60 pages.

18. "Non linear mechanics of solids", syllabus in French used during stay in University of Montpellier II, 2000, 250 pages.

19. "Dictionnaire de l'architecture et du bâtiment, français-Vietnamien". (In collaboration with Doan Nhu Kim and Doan Dinh Kien), book prepared under the sponsoring of "l'Agence Universitaire de la Francophonie" Van Hoa publisher, 1999.

20. "Proceedings of the International colloquium in Mechanics of solids, fluids, structures and interaction" August 14-18 Nha Trang, edited by LTAS-University de Liège (co-editors: F. Ronday and Nguyen Van Diep), 886 pages, 2000.

21. "Limit Analysis of Defects", (In collaboration with Staat, M.; Heitzer, M.; Yan, A.M.; Khoi, V.D.; Voldoire, F. and Lahousse, ZENTRALINSTITUT FÜR ANGEWANDTE MATHEMATIK (ZAM), Berichte des Forschungszentrums Jülich 3746, Jül-3746, (2000).

22. "Plasticity, viscoelasticity, thermoelasticity" (in French and in collaboration with Ch. MASSONNET), Lecture edited by the "Laboratoire de Mécanique des Matériaux et de Stabilité des Constructions", (1981), 340 pages.

**10.2. Journal papers (chronological order)**

1. Displacement and equilibrium methods in matrix analysis of trapezoidal structures. "Collection des Publications de la Faculté des Sciences Appliquées", n° 21, 1970.

2. Duality in the analysis of shells by the finite element method. International Journal of Solids and Structures, March 1971, vol. 7, issue 3 pp. 281-299.

3. Limit analysis of framed structures. ( in French), "Construction métallique", magazine edited by CTICM, Nr 4, 1972.

4. Limit analysis of rigid-plastic structure by a quasi-direct method ( in French) presented at "Séminaire de Plasticité et Viscoélasticité, Ecole Polytechnique de Paris", 27-29 September 1972. Published in "Sciences et Techniques de l'Armement". "Mémorial de l'Artillerie Française", 2nd section, 1973.

5. Application of the plasticity in the metal working problems (in French). "Revue de la Société Royale des Ingénieurs et des Industriels", Nr 1/2; January-February 1974, pp. 14-32.

6. Introduction to Finite element method (in French). "Annales des Travaux Publics de Belgique ", nr 1, 1973/1974.

7. Quasi-static approach of limit analysis problems (in French). "Buletinul Scientific al Institutului de Constructi ", Bucharest, Anul 17, 1974.

8. Displacement potentials for membranes on stretching and stress-function potentials for plate on bending. Ingenieur-Archiv 45 (1976), pp. 41-53.

9. Theoretical formulation and numerical efficiency of a bending finite element. ( in French and in collaboration with P. DETROUX), Collection des Publications de la Faculté des Sciences Appliquées, University of Liège, N°5, 1976, pp. 357-376.

10. Direct Limit Analysis via Rigid-Plastic Finite Element, Computer in Applied Mechanics and Engineering, vol. 8, Issue 1, April-May 1976, pp. 81-116.

11. A finite element formulation for shakedown problems using a yield criterion of the mean. (In collaboration with Jan KONIG). Computer in Applied Mechanics and Engineering, vol. 8, Issue 2, June 1976, pp. 179-192.

12. Finite element discretization and the numerical method in applied mathematics, (in French), Annales des Travaux Publics de Belgique, nr 5, 1976, and pp. 357-376.

13. Two field variational principles for Saint-Venant-von Mises material (in French) Bulletin de l'Académie Polonaise des Sciences (Warsaw). Série des sciences techniques, vol. 24, n° 7-8, pp. 325-331, 1976.

14. Plastic collapse of shells of revolution by non-linear programming and finite element techniques. Journal of Engineering Mechanics Division, ASCE, vol. 104, Nr 3, June 1978, pp. 707-712.

15. Probabilistic plastic analysis of framed structures. (In collaboration with D. FRANGOPOL), "Construction métallique", magazine edited by CTICM, Paris, Nr 1, 1977, pp. 19-43.

16. The numerical performance of a plate bending hybrid finite element. (In French and in collaboration with P. DESIR). Collection des Publications de la Faculté des Sciences Appliquées, University of Liège, Nr 66, 1977, pp. 65-123.

17. Quasi-lower bounds and upper bounds of the plastic ultimate pressure in rotationally shells by finite element methods and mathematical programming techniques (in French, in collaboration with Marc Trapletti and Daniel Ransart). International Journal of Non-linear Mechanics, edited by Prof. A. NASH, vol. 13, Issue 2, pp. 79-102, 1978.

18. Plastic strength of a reinforced double T beam subjected to bending and shearing (in French and in collaboration with CH. MASSONNET and J. JANSS), "Centre de Recherches Scientifiques et Techniques de l'Industrie des Fabrications Métalliques ", MT 126, Brussels, Belgium, September 1978.

19. New numerical experiences in shell limit analysis of revolution ( in French). ( in collaboration with D. FRANGOPOL). Science and Technique Journal of Rumania-Series of Applied Mechanics, vol. 23, Nr 4, 1978.

20. Shakedown analysis by displacement method and equilibrium finite element (in collaboration with L. PALGEN). Transactions of the CSME, vol. 6, Issue 1, pp. 32-39, 1980-81.

21. Frictionless contact of elastic bodies by finite element method and mathematical programming technique. (in collaboration with G. De SAXCE). Computers and Structures, vol 11, Issue 1-2, pp. 55-67, 1980.

22. Contact of elastic solids by finite element and mathematical programming methods. ( in French and in collaboration with G. de SAXCE). Archiwum Inzynierii Ladowej, Polish Academy of Sciences, Warsaw, 26, Nr 1, pp. 95-124, 1980.

23. On the variational principles in plasticity ( in French). "Collection des Publications de la Faculté des Sciences Appliquées", Liège, Belgium, Nr 84, 1980, pp. 59-76.

24. Finite element equilibrium analysis of creep using the mean value of the equivalent shear modulus. Meccanica (AIMETA, Italy), Nr 4, December 1980, vol. 15, pp. 234-245.

25. Analysis and optimisation of framed structures in the stable conditions. ( in French). "Construction métallique" (FRANCE), Nr 3, 1981, pp. 15-38.

26. Shakedown analysis by finite element method and linear programming techniques. "Journal de mécanique appliquée", Paris, France, vol. 2, no 4, pp. 587-599, 1983.

27. Dual analysis of frictionless contact problems by displacement and equilibrium finite element models ( in collaboration with G. DE SAXCE). Engineering Structures, Butterworth, Special number edited by NGUYEN DANG HUNG, vol. 6, Nr 1, January (1984), pp. 26-32.

28. CEPAO, an Automatic Program for Plastic Analysis and Optimisation of Frame Structures Under Stability Conditions, Engineering Structures, Special Number, edited by Nguyen Dang Hung, vol. 6, Nr 1, January (1984), pp. 33-51.

29. Applications of the mathematical programming method to structural analysis and design. Proceedings of the Workshop of Liège, 1 June 1982, Engineering Structures, Butterworth, vol. 6, Nr 1, January 1984.

30. Aspect of Analysis and Optimisation of Structures under Proportional and Variable Loadings. Engineering Optimisation, vol. 7, Nr 1, pp. 35-77 (1983).

31. An Automatic Method for the Displacement Elastic-Plastic Calculation at Plastic Collapse State-Method Using Linear Programming Technique ( in French). "Construction métallique", Nr 1, 1983, pp. 27-36.

32. A Direct Method for Information Analysis at Plastic Collapse State ( in French). "Annales de la Faculté Polytechnique, University of Kinshasa, Zaire, vol. III, IV, V, June 83/84/85, pp. 37-54.

33. Further Aspects of Analysis and Optimisation of Structures Under Proportional and Variable Loading. "Annales de la Faculté Polytechnique", University of Kinshasa, Zaire, vol. III, IV, V, June 83/84/85, pp. 1-6.

34. Dual analysis of frictionless problems by displacement and equilibrium finite elements,

Engineering Structures, (In collaboration with Géry de Saxcé), Volume 6, Issue 1 , January 1984, Pages 26-32.

35. CEPAO-an automatic program for rigid-plastic and elastic-plastic analysis and optimization of frame structures, Engineering Structures , Volume 6, Issue 1 , January 1984, pp 33-51.

36. The geometric nature of plasticity laws (In collaboration with Géry de Saxcé), Engineering Fracture Mechanics, Volume 21, Issue 4 , 1985, Pages 781-798

37. Introduction à la mécanique de la rupture ( in French). Annales des Travaux Publics de Belgique, N° 4, 26 pages (1988).

38. Modified Formula for three-dimensional Direct Stress-Intensity Factor Computation ( in collaboration with G. DE SAXCE). Communication. in Appl. Num. Meth.", Vol. 6, pp 223-230 (1989).

39. The computational of 2-D stress intensity factors using hybrid-mongrel displacement finite element. (in collaboration with G. DE SAXCE and KANG CHI HANG), Engineering Fracture Mechanics Volume 38, Issues 2-3 , 1991, pp 197-205.

40. Stress intensity factors and crack extension in a cracked pressurised cylinder. (in collaboration with Yan A.M.), Engineering Failure Analysis, Vol 1, Issue 4, pp 307-315, December 1994.

41. Elastic analysis of the multiple-cracked structure by DBEM. (in collaboration with Yan, A.M). Compte rendu du 3ème Congrès national belge de Mécanique théorique et appliqué. Liège, May, pp 1-4, 1994.

42. Multiple-cracked fatigue crack growth by BEM, (in collaboration with Yan A.M.), Computational Mechanics, Vol. 16, No. 5, pp273-280, (1995).

43. Simulation du délaminage des stratifiés par des éléments d'interface ( in collaboration with BUI A.V). Journey of FNRS, Louvain-la-Neuve, March 1997.

44. Analyse limite des structures fissures (in collaboration with YAN A.M). Journey of FNRS, Louvain-la-Neuve, March 1997.

45. Limit analysis and shakedown computation of shells and elbows (in collaboration with BORLEE B). Journey of FNRS, Louvain-la-Neuve, March 1997.

46. An enhanced elbow element - application in limit state analysis. (In collaboration with Yan A-M and Jospin R.J). Int. Journal of Num. Meth. Engng. Vol.46, 409-431, 1999.

47. Practical estimation of the plastic collapse limit of curved pipe subjected to complex loading (in collaboration with Yan A.M. and Gilles Ph). Structural Engineering and Mechanics, pages 241-438, Vol.8, N°4, 1999.

48. Limit analysis of cracked structures by mathematical programming and finite element technique (in collaboration with Yan A-M). Computational Mechanics, Springer-Verlag, pages 319-333, Vol 23, 1999.

49. Imperfect interlaminar interfaces in laminated composites: bending buckling and transient response (in collaboration with Q.V. Bui and E. Maréchal) Comp Sci Techol, 1999; 59, pp: 2269-77.

50. Imperfect interlaminar interfaces in laminated composites: interlaminar stresses and strain-energy release rates, (In collaboration with V. Q. Bui and E. Maréchal), Composites Science and Technology, Volume 60, Issue 1 , 1 January 2000, pp 131-143.

51. Direct finite element kinematical approaches in limit and shakedown analysis of shells and elbows ( in collaboration with Yan A-M), pp. 233-254, "Inelastic Analysis of Structures under Variable Loads, Theory and Engineering Applications", published by Kluwer Academic Publishers, 2000.

52. Imperfect interlaminar interfaces in laminated composites: delamination with the R-curve effect, (In collaboration with V. Q. Bui and E. Maréchal), Composites Science and Technology Volume 60, Issue 14 , November 2000, pp 2619-2630;

53. A finite-element model of mixed-mode delamination in laminated composites with an R-curve effect (in collaboration with A.M. Yan and E. Maréchal). Composites Science and Technology 61, 2001, pp 1413-1427.

54. Kinematical shakedown analysis with temperature-dependant yield stress ( in collaboration with Yan A.M) Int. J. Numer. Meth. Engng., 2001; 50:pp1145-1168.

55. A truly meshless Galerkin method based on moving least squares quadrature (in collaboration with Duflot Marc). Communication in International Journal for Numerical Methods in Engineering, N°18, pp 441-449 (2002).

56. Dual analysis by a meshless method (in collaboration with Duflot Marc). Communications in Numerical Methods in Engineering, N°18, pp 621-631 (2002).

57. Analysis of cracked plate bending by using a metis element. (In Vietnamese and in collaboration with Tran Thanh Ngoc). Revue Construction, Vol. 7, 2002, p 22-25.

58. Analysis of cracked plate membrane problem using a metis element model (in collaboration with Tran Thanh Ngoc). Vietnam Journal of Mechanics, vol 24, 2002, N°4, pp 249-256.

59. Kinematical formulation of limit and shakedown analysis ( in collaboration with Yan A. M., Khoi V. D.), NIC Series Volume 15: Numerical Methods for Limit and Shakedown Analysis , John von Neumann Institute for Computing, Jülich, Edited by Manfred Staat and Michael Heitzer, 2003, pp 85-103.

60. A dual form for discretized kinematic formulation in shakedown analysis. (in collaboration with VU D.K. and Yan A.M.). Int. Journal of Solids and Structures, Vol 41, Issue 1 pp 267-277, Pergamon, 2003.

61. On the construction of a protection structure against the coastal erosion of Ham Tien - Mui Ne, Province of Binh Thuan, Vietnam (in Vietnamese, collaboration with Nguyen Van Mao, Water Resources University of Hanoi). Journal of Resources & Environment Engineering Nr 1, pp 25-36, June/2003.

62. Analysis of cracked plates and shells using "metis" finite element model". (in collaboration with Tran Thanh Ngoc). Finite Elements in Analysis & Design (Elsevier), Volume 40, Issue 8, pp. 855-878, May 2004.

63. A primal-dual algorithm for shakedown analysis of structures (in collaboration with Vu D.K. and Yan A.M.). Computer Methods in Applied Mechanics and Engineering (Elsevier), Vol. 193/42-44 pp. 4663-4674, May 2004.

64. Fatigue crack growth analysis by an enriched meshless method (in collaboration with Marc Duflot), Journal of Computational and Applied Mathematics , Volume 168, Issues 1-2 , 1 July 2004, pp 155-164.

65. An object-oriented extended finite element module with embedded automatic mesh database, in collaboration with Bordas S., Nguyen P., Dunant C., Bonnaz R., and Guidoum A., International Journal for Numerical Methods in Engineering, submitted September 2005.

66. Architecture trade-offs of embedded meshers for extended finite element methods, in collaboration with Dunant C., Bordas S., Nguyen Vinh P., and Guidoum A., International Journal for Numerical Methods in Engineering, submitted September 2005.

67. A posteriori error estimates for the extended finite element method, in collaboration with Bordas S., Nguyen P., Nguyen Vinh P., Dunant C. and Guidoum A., Computer Methods in Applied Mechanics and Engineering, in preparation

68. Parameter study on the extended finite element method for linear elastic fracture mechanics, in collaboration with Bordas S., Nguyen P., Nguyen Vinh P., Truong Quang Tri, Dunant C. and Guidoum A., Computer Methods for Applied Mechanics and Engineering, in preparation.

**10.3. Conference proceedings (chronological order):**

1. Generalization of the dual approach in the analysis of shells by the finite element method. Presented at NATO seminar LINEC, Lisbon, Portugal, September 1971.

2. Limit analysis of shells of revolution by F.E.M. (in collaboration with D. RANSART), WCOSE Proceeding (World Congress of IASS on enclosure structures), July 1976, Montreal, Canada, pp. 471-479.

3. Duality and monotony of the two-field finite elements in elastic stress calculations. (in collaboration with P. DESIR, P. DETROUX and D. FRANGOPOL). Proceedings of 6th Canadian Congress on Applied Mechanics, Vancouver, Canada, pp. 1025-1026, 1977.

4. Application of the F.E.M. and the programming techniques in limit analysis of shells of revolution, ( in French), Colloquium of Numerical methods in Engineering Mechanics, "Ecole Centrale des Arts et Manufactures", 92290 CHATENAY-MALABRY, France.

5. A probabilistic approach for checking safety of centrally loaded steel columns. Preliminary report, Colloquium on the stability of steel structures, Liège, Belgium, pp. 113-118, 1977.

6. Dual and direct limit analysis by F.E.M. Proceedings of the 6th Canadian Congress on Applied Mechanics, Vancouver, Canada, pp. 981-982, 1977.

7. Reliability analysis and optimum probability based design of plastic structures. (in collaboration with D. FRANGOPOL and J. RONDAL). Paper presented at 14th International Congress on Theoretical and Applied Mechanics, 30 August- 4 September 1976, and Delft, NETHERLANDS. Published in Bulletin de l'Académie Polonaise des Sciences, (Warsaw), série des sciences techniques, vol. 26, Nr 5, 1978.

8. On a special class of hybrid finite elements: the "metis" (in French). Proceedings of the 1st International Congress of GAMNI, (E. ABSI and R. GLOWINSKI), Dunod technique, 1979, pp. 53-63.

9. Implementation of the duality in the finite element analysis of shells: a mixed-metis planar shell element. (in collaboration with P. DETROUX, Ph. FALLA and G. FONDER). Proceedings of World Congress on Shell and Spatial Structures, Theme 4, pp. 4.1. -4.19. Madrid, September 1979.

10. Shakedown analysis by displacement method and equilibrium finite element. (in collaboration with L. PALGEN). Proceedings of the 5th International 1979, Div. L, Section L3, Methods 1.

11. On the monotony and the convergence of a special class of hybrid finite elements. The Metis elements. Variational Methods in the mechanics of solids. Proceedings of the IUTAM symposium held at Northwestern University, Evanston, Illinois, U.S.A., edited by S. NEMAT NASSER, Pergamon Press, 1980 (pp. 208-213).

12. Shakedown analysis by F.E.M. - Force method and Displacement method. (in collaboration with L. PALGEN). Proceedings of the colloquium on the topic "Materials and Structures under Cyclic loadings, Ecole Nationale des Ponts et Chaussées, Paris, France, July 1979, pp. 250-264.

13. Numerical shakedown analysis of plates and shells of revolution. (in collaboration with P. MORELLE). 6th International Conference on Structural Mechanics in Reactor Technology, 17-21 August 1981, Paris, Session L10/4, Proceedings of the 3rd congress and exhibition of finite element methods. Beverly Hills, California, 12-16 October 1981.

14. Finite element analysis of contact problems, based on the unilateral constraints formulation. (in collaboration with G. de SAXCE and G.M.L. GLADWELL). Proceedings of the International Symposium of Structural Control. University of Waterloo, Ontario, Canada, (4 July 1979), edited by H.H.E. LEIPHOLZ, pp. 341-373, North-Holland, 1980.

15. Efficient Solution of Plastic Collapse Analysis and Optimum Design of Steel Frame Structures with Taking Account of Instability. (in collaboration with Ch. MASSONNET). The Michael R. Horne Conference (20-22 Sept. 1983) on the Instability and Plastic Collapse of Steel Structures, 98 p. (1983).

16. On the Stress intensity Factor Calculations Using the Quarter-Point Isoparametric Element... (in collaboration with G. DE SAXCE). Transactions of the 10th Int. Conf. Struct. Mech. Reactor Technology, Anaheim, California, August 14-18, (1989) page 203 vol. G.

17. Une Deduction Complète du Comportement Plastique à partir des Considérations thermodynamiques. Belgian National Congress of Theoretical and Applied Mechanics, Brussels, 1990.

18. Analyse Limite des Coudes par une Formulation Cinématiquement Admissible. ( In collaboration with R. JOSPIN). Belgian National Congress of Theoretical and Applied Mechanics, Brussels, 1990.

19. Plastic Shakedown Analysis. (in collaboration with P. Morelle). CISM courses and LECTURES Nr 299: Mathematical Programming Methods in Structural Plasticity edited by D.L. SMITH, Pringer-Verlag (1990), pp 181-205.

20. Optimal Plastic Design and the Development of Practical Software. (in collaboration with P. Morelle). CISM courses and LECTURES Nr 299: Mathematical Programming Methods in Structural Plasticity edited by D.L. SMITH, Pringer-Verlag (1990), pp 207-229.

21. Direct limit analysis of elbows by finite element and mathematical programming. (in collaboration with R.J. JOSPIN and G. DE SAXCE), Anisotropy and localisation of plastic deformation, Proceed. Symp. Plasticity 91, Grenoble, France, Edited by BOEHLER J.P. and KHAN A.S, pp. 623-626, 1991.

22. Shakedown analysis of structures, Proceed. Int. Conf. Steel & Aluminium (Addenum), Singapore May 1991, Elsevier Appl. Sc., Edited by S. L. Lee and N. E. Shanmungam. (1991).

23. Crack closure studies of bending plate using a mongrel singular finite element. (in collaboration with KANG CHI HANG, Z. Q. FENG and G. DE SAXCE). Fracture of engineering materials and structures, Proceed. edited by S.H. TEOH and K. H. LEE, Elsevier, pp 443-449 (1991).

24. A double singular finite element for cracked structures. (In collaboration with G. de Saxcé and C.H. Kang). Proceeding of the "Congrès International sur l'éducation de la pratique et la promotion des méthodes de calcul de l'ingénieur utilisant les micro-ordinateurs". Dalian, Chine, July 1992.

25. Limit and shakedown minimum design of the plane steel frames. (In collaboration with G. de Saxcé). Proceed. of the first European Conference on Numerical Methods in Engineering, 7th to 11th September 1992, Numerical Method in Engineering '92, Edited by Ch. Hirsch, O.C. Zienliewicz et E. Onate, 1992, pp 773-778.

26. Thermodynamic aspects of the plasticity. Proceedings of Int. Conf. Ho Chi Minh City 27-29 December 1995, Part II, Ho Chi Minh City Mathematical Society, vol. 5, 1995, 470-496.

27. Sur quelques expériences de coopération universitaire avec le Vietnam (in French). Workshop on Engineering Education in Developing Countries, Proceedings of the Conference of European Schools for Advanced Engineering Education and Research (CESAER), Liège 29-30 March, 1993.

28. Automatic design of frame structures under variable loadings, Proceedings of the TEMPUS Workshop and International advances Course of Budapest on Computer Aided Design of Structures, June 24-25, (1993).

29. Crack Extension of internally pressurized multiple cracked cylinder by boundary element method (in collaboration with Yan A.M.). Proceedings of the Saclay International Seminar on Structural Integrity (SISSI), Tome 2 - Posters, pp 69-74 April (1994).

30. Comparative study of virtual crack extension method and equivalent domain integral method applied to cracked structures with thermal loadings. (In collaboration with Bui, C.T). Compte rendu du 3ème Congrès national belge de Mécanique théorique et appliquée, Liège. May, pp 5-9, (1994)

31. Fatigue crack growth studies using dual boundary element method. Proceedings of the Conf. "Advances in Computational mechanics", edited by M. Papadrakakis and B.H.V. Topping, Civil-Comp Ltd, Edinburgh, Scotland, pp 301-310, September (1994).

32. Limit and shakedown analysis of axisymetrical shell by Mathematical programming. (In collaboration with BUI C.T.), LTAS- Fracture Mechanics of Solids, December, 1994.

33. Numerical comparative studies of the Rice and Bui integrals and the stress intensity factors using a double singular metis finite element. (In collaboration with Nguyen D.T.), LTAS- Fracture Mechanics of Solids, March, 1995.

34. Effet du facteur caractéristique sur le moment limite du coude soumis à la flexion plane. (In collaboration with Yan A.M), 2nd report, FRAMATOME-LTAS, LTAS- Fracture Mechanics of Solids, April 1995.

35. Multiple-cracked fatigue crack growth by Boundary Element Method. (In collaboration with Yan A.M). Proceeding of the Third Word Congress on Computational Mechanics, Chiba, Japan, August 1-5, volume I, pp 839-840, 1994, published in Computational Mechanics, edited by S.N. Atluri, 16, pp 273-280 Springer International, August, 1995.

36. Determination of singularity order and development if a metis finite element for the phenomena of delamination in composite laminates. (In collaboration with P. Schils, G. de Saxcé, S. Babric). Proceeding of the International Conference on Composite Materials and Energy, Fracture II, pp 148-155, Montréal, Canada, 8-10, May, 1995.

37. Simulation of the Crack Growth of 3D Structures under Fatigue in Taking Account of Residual Stresses, in collaboration with M SCIBETTA and B BORLEE, Proceedings of the Eleventh Biennial European Conference on Fracture, held at ENSMA Poitiers, Futuroscope, France, September 3-6, 1996. Editor: J. Petit, Co-Editors: J. de Fouquet, G. Henaff, P. Villechaise and A. Dragon, ECF 11 - Mechanisms and Mechanics of Damage and Failure,

38. Estimation Scheme for Surface Cracked Pipings Under Complex Loading: Part II: Complex Shaped Elbow Solutions, in collaboration with P GILLES and C. BOIS. Proceedings of the Eleventh Biennial European Conference on Fracture, held at ENSMA Poitiers, Futuroscope, France, September 3-6, 1996. Editor: J. Petit, Co-Editors: J. de Fouquet, G. Henaff, P. Villechaise and A. Dragon

39. Alternative estimations of interlaminar stresses using generalised laminate finite element. (In collaboration with Putz Philippe and Lambert Eric). MMSP'96 general Worshop, Proceed. of general COST 512 worshop on modelling in Materials science and processing, Davos 29.9 to 2.10.1996, pp 366.

40. Risk for cracking in multi-pass weldments. L.E. Lingren, H. Runnemalm, (in collaboration with B. Borlée,). MMSP'96 general Worshop, Proceed. of general COST 512 workshop on modelling in Materials science and processing, Davos, October, 1996.

41. Limit analysis and shakedown computation of shells and elbows. (In collaboration with Yan Ai-Min). Proceeding of the International conference EMT'97, Engineering mechanics today, Hanoi, August 1-3, 1997.

42. A damage model for mode I delamination in composites. (In collaboration with Bui Quoc Viet). Proceeding of the International conference EMT'97, Engineering mechanics today, Hanoi, 1-3 August 97.

43. A finite element formulation for shakedown analysis using the weighed average criterion. (In collaboration with Bui Cong Thanh). Proceeding of the International conference EMT'97, Engineering mechanics today, Ho Chi Minh City, 14 August, 97.

44. Plastic collapsed of curved pipe and shell by finite element method and mathematical programming technique. (In collaboration with Yan Ai-Min). IASS International Colloquium on Computation of Shell and Spatial Structures, Taipei, Taiwan, November 5-7, 1997.

45. Internal effect on the limit load of elbows. Proceeding of International Symposium of IASS, Singapore, 10-14 November 97.

46. Shakedown of structures by improved Koiter's theorem. (In collaboration with Yan A-M). Proceeding of 4th National Congress on Theoretical & Applied Mechanics, Leuven, May 22-23, pp 449-452, 1997.

47. A modified Koiter's shakedown formulation. (In collaboration with Yan A-M) Colloquium of EUROMECH 385 (8-11, Sept., Aachen, Germany), pp 83-85, 1998.

48. Limit state of cracked structures by direct mathematical programming technique. (In collaboration with Yan A-M). Advanced Computational Methods in Engineering (Proceeding of ACOMEN'98), Shaker Publishing B. V. The Netherlands, pp187-194, 1998.

49. Shakedown of Structure under thermal and mechanical loading. (In collaboration with Yan A-M). Constitutive and Damage Modelling of inelastic deformation and phase transformation - Proceeding of Plasticity'99, Cancun, Mexico, (ed. Akhtar S. KHAN), Neat Press, Fulton, Maryland, pp773-776, 1999.

50. Delamination of multi-layered composites by interface finite elements. (In collaboration with A.M. Yan and E. Maréchal). Proceed. of APCOM'99 - fourth Asia-Pacific Conf. on Computational Mechanics, Vol. 1, Singapore, pp 249-254, Computational Mechanics for next millennium, Edited by C. M .Wang, K.H. Lee and K. K. Ang, September 1999, Elsevier.

51. Modelling R-curve effects in delamination damage mechanism. (In collaboration with Q.V. Bui ET E. Maréchal). CCM12 Conference, Paris, July, paper 124, 2000.

52. Elastic-plastic analysis of structures using a displacement incremental two-field national principle. (In collaboration with Nguyen Dinh Gang). IMPLAST 2000, 7th symposium on structural failure and plasticity in Melbourne Australia, 4-6 October 2000.

53. A new truly meshless Galerkin method. (In collaboration with Marc Duflot). Proceedings of Nha Trang'2000 International Colloquium, August 2000, pp 433-442.

54. Invariant isoparametric metis displacement element. ( in collaboration with Thi D. Dang). Proceedings of Nha Trang'2000 International Colloquium, August 2000, pp 468-489.

55. Mixed-mode delamination in laminated composites with R-curved effect... (In collaboration with Yan Ai-Min). Proceedings of Nha Trang'2000 International Colloquium, August 2000, pp 443-452.

56. A general BEM for analysis of slope stability. (In collaboration with Jiang Yansheng and Wilson VENTURINI) Proceedings of Nha Trang'2000 International Colloquium, August 2000, pp 512-519.

57. Three-dimensional slope stability analysis by direct boundary element method. (In collaboration with Do Quang Khanh and Jiang Yansheng). Proceedings of Nha Trang'2000 International Colloquium, August 2000, pp819-828.

58. A programme of boundary element method for 3D elastic solids on a personal computer. (In collaboration with Do Quang Khanh and Jiang Yansheng). Proceedings of Nha Trang'2000 International Colloquium, August 2000, pp 539-443.

59. Limit load and deformation estimates by equilibrium back stress field's analysis. (In collaboration with Yan Ai-min and Vu Duc Khoi). Proceedings of Nha Trang'2000 International Colloquium, August 2000, pp 520-530.

60. Prévision de forme des pièces céramiques après séchage et cuisson. (In collaboration with Nguyen-Dai Quy). Proceedings of Nha Trang'2000 International Colloquium, August 2000, pp 636-644.

61. Simulation, calculation of mattress of placed blocks for pitched slope protection by SAMCEF-MECANO. (In collaboration with Nguyen Chien Thang and Doan Duc Bao). Proceedings of Nha Trang'2000 International Colloquium, August 2000, pp 848-857.

62. Initiation and propagation of mixed-mode interlaminar cracks in composite samples. (In collaboration with A.M. Yan and E. Maréchal). Proceedings of the 2nd European Conference on Computational Mechanics, June 26-29, 2001, Cracow, Poland, 15 pages, section 27.

63. A new dual shakedown analysis of structures. (In collaboration with V.D. Khoi and A.M. Yan). Proceedings of the 2nd European Conference on Computational Mechanics, June 26-29, 2001, Cracow, Poland, 16 pages, section 21.

64. Incremental Plasticity Limit of Structures Subjected to variable loading. (In collaboration with Ai-Min Yan and V.D. Khoi). Proceedings of the 8th International Conference on Enhancement and Promotion of Computational Methods in Engineering Science, July 2001, Shanghai, 10 pages.

65. Finite Element Modelling of Delamination of Laminated Composites, (in collaboration with Ai-Min Yan). Proceedings of the 8th International Conference on Enhancement and Promotion of Computational Methods in Engineering Science, July 2001, Shanghai, 10 pages.

65. Limit analysis of 2D Curved beams by linear optimisation programming. (In collaboration with Vo Vinh Bao and Nguyen Luu Nam Hai). Proceed. Nat. Conf. Eng. Mechanics, Hanoi, October 12-13 (2001), pp 10-20.

67. Modeling of the interactions between interlocking blocks, soil and water of pitched dike revetment using SAMCEF software. (In collaboration with Nguyen Van Hieu and Doan Duc Bao). Presented at the Phan Rang Conference organised by Vietnamese Society of Mechanics of Fluids (July 22-23, 2002).

68. Stresses singularity order in the delamination of composite laminate. (In collaboration with Nguyen Tien Duong, Hanoi University of Technology). Proc. 7th Nat. Congr. on Mech., Hanoi, December 18-20, 2002, pp 151-159.

69. A numerical tool useful for the calculation of three-dimensional crack propagation by finite element method: the fissbox. (in collaboration with Tran Duc Han and Chau Dinh Thanh, EMMC Centre, Ho Chi Minh University of Technology). Proc. 7th Nat. Congr. on Mech., Hanoi, December 18-20, 2002, pp 204-211.

70. Comparative analysis for block mattresses devoted to seashore protection. (In collaboration with Nguyen Xuan Nhi). Proc. 7th Nat. Congr. On Mech., Hanoi, December 18-20, 2002, pp 254-261.

71. Analysis of uncracked and cracked plate bending problem using metis finite element model... (In collaboration with Tran Thanh Ngoc, Nguyen Tai Trung). Proc. 7th Nat. Congr. On Mech., Hanoi, December 18-20, 2002, pp 262-270.

72. Development of a metis finite element model of shell problem with or without crack. (In collaboration with Tran Thanh Ngoc, Nguyen Tai Trung). Proc. 7th Nat. Congr. On Mech., Hanoi, December 18-20, 2002, pp 271-279.

73. Determination of the toughness of the quasi-3D structure by using the metis finite element model. (In collaboration with Do Van Truong). Proc. 7th Nat. Congr. on Mech., Hanoi, December 18-20, 2002, pp 622-633.

74. Investigating three kind of plane contact problem by penalty method.. (In collaboration with Trinh Bach Tuyet, Ho Chi Minh University of Architecture). Proc. 7th Nat. Congr. on Mech., Hanoi, December 18-20, 2002, pp 690-696.

75. Application of the SAMCEF-MECANO to the modelling of the interaction between concrete block mattresses, elastic foundation and waves. (in Vietnamese, collaboration with Nguyen Van Hieu and Doan Duc Bao), Proceeding of the seminar on the "Coastal Protection of sea and river", pp 77-94, Union of Vietnamese Sciences and Technology associations, Hanoi, November 14/2003.

76. Strength of the steel net assemblage of concrete block mattresses used as coastal cover in Mekong River, Long Xuyen, Vietnam. (In Vietnamese, collaboration with Nguyen Van Hieu and Chau Dinh Thành). Proceeding of the seminar on the "Coastal Protection of sea and river", pp. 123-138, organised by Union of Vietnamese Sciences and Technology associations and University of Water Resource of Hanoi, November 14/2003.

77. Global error estimation with displacement and equilibrium meshless methods. (In collaboration with Marc Duflot). Proceedings of the Sixth World Congress on Computational Mechanics in conjunction with Second Asian-Pacific Congress on Computational Mechanics Beijing, China, September 5-10, 2004, published by Z.H. Yao, M.W. Yuan and W.X. Zhong, Tsinhua University Press and Springer, page 316-321, 2004.

78. Duality in kinematic approaches of Limit and Shakedown Analysis of Structures. (In collaboration with Yan A.M. and Vu D.K.). Published in the book "Complementary, duality and symmetry in nonlinear mechanics", proceed. of Shanghai IUTAM Symposium, Edited by David Gao, Kluwer Ac. Publ., pp 128-148, 2004.

79. Using metis model to solve torsion problem of prismatic bar. (In collaboration with Nguyen Tien Duong). The 7th National Congress on Deformation Solid Mechanics - Do Son, Vietnam 27-28 August 2004.

80. Calculation of free edge stress for composite laminates by metis element method. (In collaboration with Nguyen Tien Duong). International Conference: Mécanique pour l'Ingénieur 2004 - Ho Chi Minh City Vietnam August 16-20, 2004.

81. Direct and indirect Métis element methods for edge delamination in laminates. (in collaboration with Nguyen Tien Duong). COMPUTATIONAL MECHANICS WCCM VI in conjunction with APCOM'04, Sept. 5-10, 2004, Beijing, China Ó 2004 Tsinghua University Press & Springer-Verlag.

82. Duality in meshless methods. (In collaboration with Marc Duflot). Proceeding of the 7th National Congress on Deformation Solid Mechanics - Do Son, Vietnam 27-28 August 2004.

**10.4. Reports (chronological order):**

1. On the Statistic Model of Atom (Quantum Mechanic) (Master Thesis in French). Faculty of Sciences, Laboratory of Theoretical Physics (Prof. Pirenne), University of Liège, (1966).

2. Digital computation of stresses and deflections in a box beam. A performance comparison between finite element models and idealisation patterns (in collaboration with G. SANDER and P. BECKERS). Technical Report AFFDL-TR-69-4, January 1969. Collection des Publications, Nr 4, page 87, 1967.

3. Natural strains and stresses for trapezoidal structures analysis (in collaboration with Professor B. FRAEIJS DE VEUBEKE). 37 p., 6 figures, Technical Report AFFDL-TR-69-18, February 1969.

4. Foundation of the finite element method. Report Nr 42 in French. Laboratory of Strength of Materials and Stability of Constructions, University of Liège, 1971.

5. A new interpretation of KOLOSOV-MUSKHELISHVILI functions for plane problems in elasticity. Displacement formulation. Report Nr 12, Laboratory of Strength of Materials and Stability of Constructions University of Liège, 1972. Presented at French Congress of Mechanics, 17-20 September 1973, Poitiers, France.

6. Mechanics of the behaviour of the non-elastic material. Post-graduate course (in French) "Laboratoire de Mécanique des Matériaux et de stabilité des Constructions, Liège", 140 p. (1980).

7. Finite element solutions of unilateral problems, (in French). September 1980. Laboratoire de Mécanique des Matériaux et de Stabilité des Constructions, Liège, Belgium.

8. Data preparations and output explanations of the program CEPAO (in French). (In collaboration with R. BALTUS, G. de SAXCE, and E. LEMAIRE). Report Nr 109. Laboratoire de Mécanique des Matériaux et de Stabilité des Constructions, 1980.

9. A thermodynamic model for the contact problems of solids (in French and in collaboration with G. de SAXCE). Report Nr 103, Laboratoire de Mécanique des Matériaux et de Stabilité des Constructions- 1980.

10. A metis finite element with arbitrary stress field included a singular field for fracture. Report Nr 111, September 1981, Laboratoire de Mécanique des Matériaux et Statique des Constructions, University of Liège.

11. User's Guides of CEPAO-82 - Computer Program for Analysis and Stable Design of Elastic-Plastic Structures - Data preparation. ( In collaboration with G. DE SAXCE, E. LEMAIRE et P. VILLERS), report Nr 127, "Laboratoire de Mécanique des Matériaux et Statique des Constructions, Université de Liège", 80 p., Novembre (1982).

12. On the Simplex Algorithm in CEPAO-82. Report Nr 133. Laboratoire de Mécanique des Matériaux et Statique des Constructions, Université de Liège, March 1983.

13. Cyclic Loading Studies of General Hardening Models, Report Nr 138. Laboratoire de Mécanique des Matériaux et Statique des Constructions, Université de Liège. December 1983.

14. On the Plasticity and the Calculation of Limit States by F.E.M. (in French). Thesis of the degree of "Agrégation" or Special Ph. D. - "Faculté des Sciences Appliquées, Université de Liège, Collection des Publications" Nr 98, 1985.

15. Evaluation des facteurs d'intensité de contrainte des structures à 3 dimensions ( in collaboration with G. DE SAXCE). Internal report, Nr 175, 45 pages (1988), Depart. M.S.M., University of Liège.

16. Automatisation de maillage en front de fissure. ( In collaboration with G. DE SAXCE), Internal report Nr 178, 32 pages (1988), Department M.S.M., University of Liège.

17. Evaluation du taux de restitution d'énergie des structures fissurées à 3 dimensions. (In French, in collaboration with G. DE SAXCE). Internal report Nr 179, 35 pages (1988), Department M.S.M., University of Liège.

18. Manuel d'utilisation du logiciel SAMCEF pour la résolution des problèmes tridimensionnels de mécanique de la rupture. Final report, SEP-SAMTECH-MSM, Nr 190, March 1989, SAMTECH-MSM, Université of Liège.

19. Analyse Limite des Coudes par la Méthodes des Eléments Finis et la Programmation Mathématique. (In collaboration with R. JOSPIN). Internal report MR-01/90, LTAS - Fracture mechanics of solids, December 1990.

20. Maillage automatique d'une boîte fissure. Internal report LTAS- Fracture Mechanics of Solids, Nr MR-02/90, January 1991, 30 pages, 1991.

21. Estimation de l'intégrale J élastique et élasto-plastique par la méthode du domaine de l'intégration équivalente (EDI). (In collaboration with KANG CHI HANG). Internal report LTAS-Mécanique de la Rupture, University of Liège, January 1992.

22. Limit analysis of elbows using Finite Element Method and Mathematical Programming Techniques. Report "Limit loads of pipe elbows, contact RA1-0134B", (in collaboration with M. Save and R. Jospin).

23. On the shakedown theorems and the finite element computation of the shakedown limit loads. Internal report LTAS- Fracture Mechanics of Solids, June, 1994.

24. Modeling du Délaminage par la Mécanique de l'Endommagement.. In French (in collaboration with E. Lambert, G. Laschet, G de Saxcé), section B of the 1st report: "Développement et validation de modèles pour la caractérisation des propriétés mécaniques et Multimatériaux" project sponsored by Walloon Region, LTAS- Fracture Mechanics of Solids, March, 1994.

25. Génération linéaire d'une famille d'éléments fins d'interface. In French ( in collaboration with E. Lambert, G. Laschet, G de Saxcé), section B of the2nt report: "Développement et validation de modèles pour la caractérisation des propriétés mécaniques et la description des mécanismes d'endommagement de structures en matériaux composites", Convention N° 2397, project sponsored by Walloon Region, LTAS-Fracture Mechanics of Solids, November, 1994.

26. Limit loads of pipe and elbows (in collaboration with M. Save R.J. Jospin). European commission, nuclear science and technology, Final report, EUR 15696EN, 1995.

27. Calcul des charges limites des coudes par un élément fini de poutre et par la méthode de programmation mathématique. (In collaboration with Yan A.M.), report N° 1, FRAMATOME-LTAS, LTAS- Fracture Mechanics of Solids, February 1995.

28. Modélisation et simulation de la croissance d'endommagement et de fissuration des structures métalliques et composites soumises à la fatigue et en présence des contraintes résiduelles. (in collaboration with B. Borlée, B. De Bel, Ph. Putz). First report, COST 512, Convention 2670 sponsored by Walloon Region, LTAS- Fracture Mechanics of Solids, March, 1995.

29. Limit analysis and shakedown computation of shells and elbows (in collaboration with YAN A.M and BUI CONH THANH.). Internal report N° R96-2-1. February 1996.

30. Modélisation et simulation de la croissance d'endommagement et de fissuration des structures métalliques et composites soumises à la fatigue et en présence des contraintes résiduelles. (In collaboration with Borlée, B., De Bel B. et Putz Ph). Internal report, COST Project 512, Period from September 15.94 to March 15.95. 1995.

31. Modélisation et simulation de la croissance d'endommagement et de fissuration des structures métalliques et composites soumises à la fatigue et en présence des contraintes résiduelles. ( in collaboration with Borlée, B., De Bel B. et Putz Ph). Internal report, COST Project 512, Period from September 15.95 to March 15.95. 1996.

32. Modélisation du délaminage par la mécanique d'endommagement. (In collaboration with Bui Q.V). Internal report, LTAS- Fracture Mechanics of Solids, October 1996.

33. On a general method for yield criterion deduction in generalised variables. (In collaboration with Bui Cong Thanh). Internal report, LTAS- Fracture Mechanics of Solids, January 1997.

34. Application of shakedown methods to piping. (In collaboration with Bucktthorpe, P. Rathjen, H. Hoell, Y. Renault and Yan A.M). Final report, CEC/WGCS-AG2, FBR study contract RAI-0235 UK, NNC, May 1997.

35. Practical estimation of plastic collapsed limit of curved pipe subjected to complex loading. (In collaboration with Yan A.M. internal report, LTAS- Fracture Mechanics of Solids, February 1997.

36. Limit analysis of defects. (In collaboration with M. Staat, M. Heitzer, A. M. Yan, V.D. Khoi, F. Voldoire and A. Lahousse). Report N° 3746, Forschungszentrum Jülich, Institut für Sicherheitsorschung und Reaktortechnik, Brite-Euram III contract N° BRPR-CT97-059, Project BE97-4547, March, 2000.

**10.5. General papers (chronological order):**

1. Report concerning the training programme and the Vietnamese universities (1989).

2. Report concerning the activities of the university co-operation sponsored by agency FICU, AUPELF&UREF (1991).

3. The overseas Vietnamese's and the scientific co-operation with Vietnam (in Vietnamese appeared in DOAN KET). N° 418, France, November 1989.

4. Comments on the scientific co-operation with Vietnam (in Vietnamese), "TUOI TRE CHU NHAT NEWS PAPER" Ho Chi Minh City, February 25, 1990.

5. On the experiences of the university co-operation with Vietnam. Workshop on Engineering Education in Developing Countries, Proceedings of the Conference of European Schools for Advanced Engineering Education and Research (CESAER), Liege 29-30 March, 1993.

6. On the programme EMMC and the Belgian grants to Vietnamese Universities. Paper in Vietnamese published in 'TUOI TRE (Youth)", Ho Chi Minh City, Saturday, February, 24, 1996.

7. Final report of the activities of the programme EMMC (1995-1999). (In French), LTAS-Fracture Mechanics, November 1999, (See appendix).

8. EMMC et MCMC, Master training programmes located in Vietnam. Séminaire Europe organised by " Agence Universitaire de la Francophonie ", University of Evry Val d'Essonne, 25-27 March 1999.

9. Final activity report of the programme PIP-EMMC, 95-99. LTAS-Mécanique de la Rupture, November 1999.

10. Report on the feasibility of a creation of an enterprise on the domain of CAO-FEM in Vietnam. LTAS-Mécanique de la Rupture, May, 2000.

…….

**10.6. Poetry publications**

1. Time is young forever (in Vietnamese), Collection of poems in Vietnamese, edited by Hien-Dien, Liege, 1973.

2. The shadow of times (in Vietnamese), Collection of Poems in Vietnamese, edited by Thanh-Long, Brussels 1973.

3. The beaten track (in