Automatic generation of equilibrium and flexibility matrices for plate bending elements using Integrated Force Method

다국어 초록 (Multilingual Abstract)

The Integrated Force Method (IFM) has been developed in recent years for the analysis of civil, mechanical and aerospace engineering structures. In this method all independent or internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of

equilibrium and compatibility conditions. The solution by IFM needs the computation of element equilibrium and flexibility matrices from the assumed displacement, stress-resultant fields and material properties. This paper presents a general purpose code for the automatic generation of element equilibrium and flexibility matrices for plate bending elements using the Integrated Force Method. Kirchhoff and the Mindlin-Reissner plate theories have been employed in the code. Paper illustrates development of element

equilibrium and flexibility matrices for the Mindlin-Reissner theory based four node quadrilateral plate bending element using the Integrated Force Method.

참고문헌 (Reference)

1 Timoshenko, S.P., "Theory of Plates and Shells,Second Edition" McGraw Hill 1959

2 Korncoff, A.R., "Symbolic generation of finite element stiffeness matrices" 10 : 119-124, 1979

3 Nagabhushanam, J., "Symbolic generation of elemental matrices for finite elemental analysis" 42 (42): 375-380, 1992

4 Foster, K.R., "Symbolic computation programs for the personal computers" 243 : 679-684, 1989

5 Patnaik, S.N., "Structural optimization with approximate sensitivities" 58 : 407-418, 1996

6 Griffiths, D.V., "Stiffness matrix of the four node quadrilateral element in closed form" 37 : 1028-1038, 1994

7 Mbakogu, F.C., "Some applications of computer algebra to classical problems in plate theory" 27 : 348-365, 1999

8 Chee, C., "Shape function generations using MACSYMA" 16 : 705-719, 2000

9 Pavlovic, M.N., "Review article on symbolic computation in structural engineering" 81 : 2121-2136, 2003

10 Chen Wanji, "Refined quadrilateral element based on Mindlin/Reissner plate theory" 47 : 605-627, 2000

11 Krishnam Raju, N.R.B., "Non-linear structural analysis using integrated force method" 25 (25): 353-365, 2000

12 Patnaik, S.N., "Integrated force method verses standard force method" 22 (22): 151-163, 1986

13 Nagabhushanam, J., "General purpose program to generate compatibility matrix for the integrated force method" 28 : 1838-1842, 1990

14 Beltzer A.L., "Engineering analysis via symbolic computations a break through" 43 : 119-127, 1990

15 Gunderson, R.H., "Element stiffness matrix generator" 97 : 363-375, 1971

16 Noor, A.K., "Computerized symbolic manipulations in structural mechanics—progress and potential" 10 : 95-118, 1979

17 Lee, C.K., "Closed form stiffness matrix solutions for some commonly used hybrid finite elements" 67 : 463-482, 1998

18 Cecchi, M.M., "Automatic generation of stiffness matrices for the finite element analysis" 11 : 396-400, 1977

19 Nagabhushanam, J., "Automatic generation of sparse and banded compatibility matrix for the integrated force method" 20-25, 1991

20 Luft, R.W., "Automatic generation of finite element matrices" 97 : 349-362, 1971

21 Chang, T.Y., "Application of symbolic method to hybrid or mixed finite elements and computer implementation" 35 (35): 293-299, 1990

22 Patnaik, S.N., "An integrated force method for discrete analysis" 41 : 237-251, 1973

23 Jane Liu, "A four node shear-deformable shell element developed via explicit Kirchhoff constraints" 49 : 1065-1086, 2000

24 Hoa, S.V., "A computer program for automatic generation of stiffness and mass matrices in finite element analysis" 11 : 147-161, 1980