Title: Finite element structural response sensitivity and reliability analyses using smooth versus non-smooth material constitutive models

Authors: Michele Barbato, Joel P. Conte

Addresses: Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA. ' Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA

Abstract: This paper focuses on the effects upon the design point search of gradient discontinuities caused by non-smoothness of material constitutive models in the context of finite element reliability analysis. The response computation algorithm for the Menegotto-Pinto smooth material constitutive model is extended to response sensitivity analysis using the Direct Differentiation Method. Response sensitivity and reliability analysis results are compared for a structural system modelled using smooth and non-smooth material constitutive laws, respectively. Both material and discrete loading sensitivity parameters are considered. Structural reliability analyses are performed using the First-Order Reliability Method. Implications of using smooth versus non-smooth material constitutive models in finite element response, response sensitivity and reliability analyses are discussed. A sufficient condition on the smoothness of uni-axial material constitutive models for obtaining continuous finite element response sensitivities is stated and proved for the quasi-static case. The issue of continuity/discontinuity of response sensitivities for the dynamic case is discussed within the application examples.

Keywords: material constitutive models; material constitutive parameters; finite element method; FEM; response sensitivity analysis; gradient-based optimisation methods; structural reliability analysis; design point search; gradient discontinuities.

DOI: 10.1504/IJRS.2006.010688

International Journal of Reliability and Safety, 2006 Vol.1 No.1/2, pp.3 - 39

Available online: 19 Aug 2006 *

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