PFEM formalism in Kronecker notation

Mathematics and Mechanics of Solids

Volumn 1, Issue 4, 1996, Pages 445-461

  Zhang, Yimin ^a   Wen, Bangcun ^a   Chen, Suhuan ^b  

^a NORTHEASTERN UNIVERSITY   (China)

^b JILIN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTION EVALUATION; MATRIX ALGEBRA; PROBABILITY; PROBABILITY DENSITY FUNCTION; VECTORS;

FINITE ELEMENT METHOD;

EID: 0030380354     PISSN: 10812865     EISSN: None     Source Type: Journal    
DOI: 10.1177/108128659600100406     Document Type: Article

References (13)

1. Ang, A. H. S. and Tang, W. K.: Probability Concepts in Engineering Planning and Design, Volume I, Basic Principles, Wiley, New York, 1975.
2. Ma, F.: Extension of second moment analysis to vector-valued and matrix-valued functions. Int. J. of Non-Linear Mech., 22, 251-260 (1987).
3. Liu, W. K., Belytschko, T., and Mani, A.: Probabilistic finite elements for nonlinear structural dynamics. Comp. Methods in Appl. Mech. and Eng., 56, 61-81 (1986).
4. Liu, W. K., Belytschko, T., and Mani, A.: Random field finite elements. Int. J. of Numerical Methods in Eng., 23, 1831-1845 (1986).
5. Liu, W. K., Belytschko, T., and Mani, A.: Applications of probabilistic finite element methods in elastic/plastic dynamics. J. of Eng. for Industry, ASME, 109, 2-8 (1987).
6. Liu, W. K., Mani, A., and Belytschko, T.: Finite element methods in probabilistic mechanics. Probabilistic Eng. Mech., 2, 201-213 (1987).
7. Liu, W. K., Besterfield, G., and Belytschko, T.: Transient probabilistic systems. Comp. Meth. in Appl. Mech. and Eng., 67, 27-54 (1988).
8. Liu, W. K., Besterfield, G., and Belytschko, T.: Variational approach to probabilistic finite elements. J. of Eng. Mech. Div., ASCE, 114, 2115-2133 (1988).
9. Contreras, H.: The stochastic finite-element method. Computers & Structures, 12, 341-348 (1980).
10. Vanmarcko, E., Shinozuka, M., Nakagiri, S., Schueller, G., and Grigoriu, M.: Random fields and stochastic finite element methods. Struct. Safety, 3, 143-166 (1986).
11. Benaroya, H., and Rebak, M.: Finite element methods in probabilistic structural analysis: A selective review. Appl. Mech. Rev., 41, 201-213 (1988).
12. Vetter, W. J.: Matrix calculus operations and taylor expansions. SIAM Review, 15, 352-369 (1973).
13. Brewer, J. W.: Kronecker products and matrix calculus in system theory. IEEE Transactions on Circuits and Systems, CAS-25, 772-781 (1978).