Abstract
A uniform variational approach to sensitivity analysis of linear and nonlinear structures with both material and geometrical nonlinearities is presented. Arbitrary stress, strain or displacement functionals are considered, and they are augmented by the associated bilinear functionals expressed in terms of primary and adjoint fields. Their variation with respect to stress or displacement fields provides compatability or equilibrium conditions for primary and adjoint structures, whereas variation with respect to material variables or shape of the body provides sensitivity of the functional.
General results can easily be particularized to the case of beams, disks, plates or shells with external boundary or interface variation, and can be used to solve optimal design problems by iterative procedures based on optimality conditions.
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© 1986 Plenum Press, New York
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Mróz, Z. (1986). Variational Approach to Shape Sensitivity Analysis and Optimal Design. In: Bennett, J.A., Botkin, M.E. (eds) The Optimum Shape. General Motors Research Laboratories Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-9483-3_4
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DOI: https://doi.org/10.1007/978-1-4615-9483-3_4
Publisher Name: Springer, Boston, MA
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