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Design sensitivity analysis of nonlinear structures using endochronic constitutive model. II: Discretization and applications. (English) Zbl 0756.73061

Summary: The continuum formulation for design sensitivity analysis incorporating the unified endochronic constitutive model described in part 1 [see the foregoing entry] is discretized and implemented using the standard isoparametric finite element procedure. Only the total Lagrangian approach is investigated since it has been concluded to be superior to the updated Lagrangian approach. Solution of the sensitivity equation and its convergence criterion are reported. Several cases of a ten-member truss under static and dynamic loads are investigated for sensitivity verification for both nonshape and shape design problems. It is concluded that the incremental solution procedure for design sensitivity analysis of history dependent nonlinear problems can give quite accurate sensitivities. However, the equation of motion, constitutive equations and the sensitivity equations must be integrated very accurately. Thus small increments are generally needed and the computational effort for such problems can be substantial.

MSC:

74P99 Optimization problems in solid mechanics
74A20 Theory of constitutive functions in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)

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References:

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