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Shape Variations for Viscoelastic Solids Under Transient Response
Author(s) -
Meric R. A.
Publication year - 1990
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19900701108
Subject(s) - viscoelasticity , material derivative , transient (computer programming) , sensitivity (control systems) , mathematics , simple (philosophy) , transient response , mathematical analysis , variable (mathematics) , adjoint equation , integral equation , differential equation , physics , computer science , thermodynamics , engineering , philosophy , electrical engineering , epistemology , electronic engineering , operating system
Sensitivity expressions for a general performance criterion (cf. an integral functional) with respect to shape have been derived for viscoelastic solids under transient response. Differential and integral types of constitutive equations are considered in the study, in which a continuum approach is adopted. By using the material derivative concept and the adjoint variable method the sensitivity of the general integral functional is obtained in terms of primary and adjoint functions. A simple example problem is also provided to check the results by comparing them with those found by a direct differentiation.