Shape Sensitivity Analysis and Computer-Aided Design of Nonlinear Structures
Phelan, David Gerald
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https://hdl.handle.net/2142/69977
Description
Title
Shape Sensitivity Analysis and Computer-Aided Design of Nonlinear Structures
Author(s)
Phelan, David Gerald
Issue Date
1988
Doctoral Committee Chair(s)
Haber, Robert
Department of Study
Civil Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Civil
Engineering, Mechanical
Abstract
A unified approach for explicit structural design sensitivity analysis of linear and non-linear elastic systems is presented. First-order sensitivity expressions involving the complete set of design variables, including shape design parameters, are derived for general response functionals. Both direct differentiation and adjoint variable methods are developed in a general, variational context. The resulting sensitivity expressions are valid for use with approximate solutions based on any of several weak, weighted residual forms of the elasticity equations. Several illustrative examples are included.
The mixed Eulerian-Lagrangian kinematic description (ELD) is introduced for the treatment of shape variation problems and is used in both the direct differentiation and adjoint variable methods. This approach is an alternative to the material derivative methods presented in the literature. The adjoint variable derivations are based on a new energy principle. The mutual Hu-Washizu energy principle is formally stated and proved. The design sensitivity derivations based on this principle unify and extend several of the adjoint variable methods found in the literature. For geometrically nonlinear systems, the governing elasticity equations and design sensitivity problem can be described in either of two forms: the Lagrangian form or the Eulerian form. The proper form for a given application depends on the form of the independent design parameters. Governing equations and design sensitivity expressions are presented for both forms. Material nonlinearities restricted to nonlinear, elastic behavior are also treated in the derivations.
Lastly, the implementation of the structural design process and the design sensitivity methods in the context of an advanced, computer-aided design environment is discussed. Two computer programs for design sensitivity analysis and computer-aided design, developed as part of this investigation, are described.
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