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

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 constitutive model for structural steel is extended to response sensitivity analysis using the Direct Differentiation Method (DDM). Comparisons are made between response sensitivity analysis and reliability analysis results of a structural system modeled 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 (FORM). Implications of using smooth versus non-smooth material constitutive models for finite element response and response sensitivity analyses as well as reliability analysis 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. Based on application examples, remarks are made on the continuity (or lack

Effect of Constitutive Material Models on Seismic Response of Two-Story Reinforced Concrete Frame

“…7). Previous findings by some researchers also indicate the same phenomenon in the similar manner (Haukaas and Der Kiureghian 2004;Barbato and Conte 2006). Thus, the continuity of the response computation can be achieved by using smooth material models which is essential for the convergence in the search of design point in reliability analysis.…”

“…It has been suggested that by using the smooth material models such effect can be avoided. Another study was conducted focusing on the effect of gradient discontinuities caused by non-smoothness of the material models in the reliability context (Barbato and Conte 2006). A structural system was modeled using smooth and non-smooth reinforcing steels to compare response sensitivity and reliability analysis results.…”

Nonlinear stochastic dynamic analysis for performance‐based earthquake engineering

“…Subsequent publications using this approach include Der Kiureghian and Li [20], Zhang and Der Kiureghian [21], Der Kiureghian [22], Franchin [23], Koo et al [24], Jensen and Capul [25], and Barbato and Conte [26]. In a recent paper [27], the authors formalized the use of FORM for solving nonlinear stochastic dynamic problems into a new ELM.…”

“…This, in turn, requires that the nonlinear response X (t, u) be continuously differentiable with respect to u. As shown by Haukaas and Der Kiureghian [32,33] and Barbato and Conte [26], this requirement is satisfied if the transitions between material states (except for elastic unloading) are smooth. Many commonly used nonlinear material models, including the well-known class of Bouc-Wen models [14,35], satisfy this requirement.…”

Probabilistic analysis for design assessment of continuous steel–concrete composite girders

“…The constitutive parameters assumed as random parameters (i.e., the components of the vector related to the steel materials) are the modulus of elasticity, E, the yield stress, f y , and the post-yield to initial tangent stiffness ratio b. Details on the model, its numerical implementation, and response sensitivity computation can be found in [35].…”