PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

A new hybrid finite element approach for three-dimensional elastic problems

Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A new fundamental solution based finite element method (HFS-FEM) is presented for analyzing three-dimensional (3D) elastic problems with body forces in this paper. It begins with deriving formulations of 3D HFS-FEM for elastic problems without body force and then the body force term is handled by means of the method of particular solution and radial basis function approximation. In our analysis, the homogeneous solution is obtained using the proposed HFS-FEM and the particular solution associated with the body force is approximated by radial basis functions. Several standard tests and numerical examples are considered to assess the capability and performance of the proposed method and elements. It is found that, comparing with conventional FEM (ABAQUS), the proposed method can achieve higher accuracy and efficiency when same element meshes are used. It is also found that the elements associated with this method are not very sensitive to mesh distortion and can be employed for problems involving nearly incompressible materials. This new method seems to be promising to deal with problems involving generalized body force, complex geometry, stress concentration and multi-materials.
Rocznik
Strony
261--261
Opis fizyczny
-–292, Bibliogr. 43 poz.
Twórcy
autor
autor
autor
Bibliografia
  • 1. J. Jirousek, L. Guex, The hybrid-Trefftz finite-element model and its application to plate bending, International Journal for Numerical Methods in Engineering, 23, 4, 651–693, 1986.
  • 2. Q.H. Qin, Hybrid Trefftz finite-element approach for plate-bending on an elastic-foundation, Applied Mathematical Modelling, 18, 6, 334–339, 1994.
  • 3. J. Jirousek, Q.H. Qin, Application of hybrid-Trefftz element approach to transient heat-conduction analysis, Computers & Structures, 58, 1, 195–201, 1995.
  • 4. Q.H. Qin, Formulation of hybrid Trefftz finite element method for elastoplasticity, Applied Mathematical Modelling, 29, 3, 235–252, 2005.
  • 5. H. Wang, Q.H. Qin, D. Arounsavat, Application of hybrid Trefftz finite element method to non-linear problems of minimal surface, International Journal for Numerical Methods in Engineering, 69, 6, 1262–1277, 2007.
  • 6. J.A.T. De Freitas, M. Toma, Hybrid-Trefftz stress elements for incompressible biphasic media, International Journal for Numerical Methods in Engineering, 79, 2, 205–238, 2009.
  • 7. K.Y. Sze, G.H. Liu, Hybrid-Trefftz six-node triangular finite element models for Helmholtz problem, Computational Mechanics, 46, 3, 455–470, 2010.
  • 8. J.A.T. De Freitas, I.D. Moldovan, Hybrid-Trefftz stress element for bounded and unbounded poroelastic media, International Journal for Numerical Methods in Engineering, 85, 8, 1280–1305, 2011.
  • 9. Q.H. Qin, Solving anti-plane problems of piezoelectric materials by the Trefftz finite element approach, Computational Mechanics, 31, 6, 461–468, 2003.
  • 10. G.S.A. Fam, Y.F. Rashed, The Method of Fundamental Solutions applied to 3D structures with body forces using particular solutions, Computational Mechanics, 36, 4, 245–254, 2005.
  • 11. C. Patterson, M. Sheikh, On the use of fundamental solutions in Trefftz method for potential and elasticity problems, Boundary Element Methods in Engineering, Proceedings of the Fourth International Seminar, Southampton, England, Germany, 21–23 September, 1982, 43–57.
  • 12. R. Piltner, The derivation of a thick and thin plate formulation without ad hoc assumptions, Journal of Elasticity, 29, 2, 133–173, 1992.
  • 13. J. Jirousek, A. Wroblewski, Q.H. Qin, X.Q. He, A Family of Quadrilateral Hybrid Trefftz P-Elements for Thick Plate Analysis, Computer Methods in Applied Mechanics and Engineering, 127, 1–4, 315–344, 1995.
  • 14. Q.H. Qin, The Trefftz Finite and Boundary Element Method, WIT Press, Southampton 2000.
  • 15. Q.H. Qin, H. Wang, Matlab and C Programming for Trefftz Finite Element Methods, CRC Press, New York 2008.
  • 16. H. Wang, Q.H. Qin, FE approach with green’s function as internal trial function for simulating bioheat transfer in the human eye, Archives of Mechanics, 62, 6, 493–510, 2010.
  • 17. H. Wang, Q.H. Qin, Hybrid FEM with fundamental solutions as trial functions for heat conduction simulation, Acta Mechanica Solida Sinica, 22, 5, 487–498, 2009.
  • 18. H. Wang, Q.H. Qin, Fundamental-solution-based finite element model for plane orthotropic elastic bodies, European Journal of Mechanics, A/Solids, 29, 5, 801–809, 2010.
  • 19. C. Cao, Q.H. Qin, A. Yu, Hybrid fundamental-solution-based FEM for piezoelectric materials, Computational Mechanics (to appear).
  • 20. S.W. Gao, Y.S. Wang, Z.M. Zhang, X.R. Ma, Dual reciprocity boundary element method for flexural waves in thin plate with cutout, Applied Mathematics and Mechanics-English Edition, 26, 10, 1564–1573, 2005.
  • 21. M. Dhanasekar, J.J. Han, Q.H. Qin, A hybrid-Trefftz element containing an elliptic hole, Finite Elements in Analysis and Design, 42, 14–15, 1314–1323, 2006.
  • 22. S.A. Sauter, C. Schwab, Boundary Element Methods, Springer, 2010.
  • 23. C.S. Chen, C.A. Brebbia, The dual reciprocity method for Helmholtz-type operators, Boundary Elements Xx, 4, 495–504, 1998.
  • 24. A.H.D. Cheng, C.S. Chen, M.A. Golberg, Y.F. Rashed, BEM for theomoelasticity and elasticity with body force – a revisit, Engineering Analysis with Boundary Elements, 25, 4–5, 377–387, 2001.
  • 25. H. Wang, Q.H. Qin, Y.L. Kang, A new meshless method for steady-state heat conduction problems in anisotropic and inhomogeneous media, Archive of Applied Mechanics, 74, 8, 563–579, 2005.
  • 26. R.H. Macneal, R.L. Harder, A proposed standard set of problems to test finite element accuracy, Finite Elements in Analysis and Design, 1, 1, 3–20, 1985.
  • 27. J. Korelc, P. Wriggers, Improved enhanced strain four-node element with Taylor expansion of the shape functions., International Journal for Numerical Methods in Engineering, 40, 3, 407–421, 1997.
  • 28. U. Andelfinger, E. Ramm, EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements, International Journal for Numerical Methods in Engineering, 36, 6, 1311–1337, 1993.
  • 29. S.L. Weissman, R.L. Taylor, A unified approach to mixed finite element methods: Application to in-plane problems, Computer Methods in Applied Mechanics and Engineering, 98, 1, 127–151, 1992.
  • 30. S.L. Weissman, High-accuracy low-order three-dimensional brick elements, International Journal for Numerical Methods in Engineering, 39, 12, 2337–2361, 1996.
  • 31. T.H.H. Pian, P. Tong, Relations between incompatible displacement model and hybryd stress model, International Journal for Numerical Methods in Engineering, 22, 1, 173–181, 1986.
  • 32. Y.P. Cao, N. Hu, J. Lu, H. Fukunaga, Z.H. Yao, A 3D brick element based on Hu–Washizu variational principle for mesh distortion, International Journal for Numerical Methods in Engineering, 53, 9, 2529–2548, 2002.
  • 33. D.B. Ribeiro, J.B. Paiva, An alternative multi-region BEM technique for three-dimensional elastic problems, Eng. Anal. Bound. Elem., 33, 4, 499–507, 2009.
  • 34. J.C. Simo, M. Rifai, A class of mixed assumed strain methods and the method of incompatible modes, International Journal for Numerical Methods in Engineering, 29, 6, 1595–1638, 1990.
  • 35. A.H.D. Cheng, C.S. Chen, M.A. Golberg, Y.F. Rashed, BEM for theomoelasticity and elasticity with body force – a revisit, Engineering Analysis with Boundary Elements, 25, 4–5, 377–387, 2001.
  • 36. Z.C. Li, T.T. Lu, H.Y. Hu, A. Cheng, Trefftz and collocation methods, WIT Press, 2008.
  • 37. J.J. Golecki, On stress concentration around circular holes, International Journal of Fracture, 73, 1, R15–R17, 1995.
  • 38. G.N. Savin, Stress Concentration Around Holes, Pergamon Press, New York 1961.
  • 39. E.S. Folias, J.J. Wang, On the three-dimensional stress field around a circular hole In a plate of arbitrary thickness, Computational Mechanics, 6, 5, 379–391, 1990.
  • 40. D.S. Mueller-Hoeppe, S. Loehnert, P. Wriggers, A finite deformation brick element with inhomogeneous mode enhancement, International Journal for Numerical Methods in Engineering, 78, 8, 1164–1187, 2009.
  • 41. P.M.A. Areias, J.M.A. César de Sá, C.A.C. António, A.A. Fernandes, Analysis of 3D problems using a new enhanced strain hexahedral element, International Journal for Numerical Methods in Engineering, 58, 9, 1637–1682, 2003.
  • 42. J. Korelc, P.Wriggers, An efficient 3D enhanced strain element with Taylor expansion of the shape functions, Computational Mechanics, 19, 2, 30–40, 1996.
  • 43. Q.H. Qin, Postbuckling analysis of thin plates by a hybrid Trefftz finite element method, Computer Methods in Applied Mechanics and Engineering, 128, 1–2, 123–136, 1995.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0011-0054
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.