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Variational approach to first‐ and second‐order sensitivity analysis of elastic structures

1985; Wiley; Volume: 21; Issue: 4 Linguagem: Inglês

10.1002/nme.1620210405

1097-0207

K. Dems, Z. Mróz,

Structural Load-Bearing Analysis

Abstract For a linear elastic structure, the first variations of arbitrary stress, strain and displacement functionals were explicitly expressed in terms of variations of material stiffness parameters within specified domain, in References 1 and 2, by using the solutions for primary and adjoint systems. In this paper, explicit expressions for second variations are derived for the case when the material stiffness or compliance variations depend on a set of parameters. These expressions arc obtained in terms of variations of stiffness or compliance parameters by using the solutions of two additional sets of adjoint systems. Furthermore, the variation of local stress, strain or displacement is considered. Several illustrative examples are provided for the first‐ and second‐order sensitivity analysis of beams.