Consistent Finite-Element Response Sensitivity Analysis

Abstract

This paper examines the important issue of response sensitivities of dynamic models of structural systems to both material and ͑discrete͒ loading parameters. Plasticity-based finite-element models of structural systems subjected to base excitation such as earthquake loading are considered. The two methods for computing the response sensitivities, namely, ͑1͒ discretizing in time the time continuous-spatially discrete response equations and differentiating the resulting time discrete-spatially discrete response equations with respect to sensitivity parameters, and ͑2͒ differentiating the time continuous-spatially discrete response equations with respect to sensitivity parameters and discretizing in time the resulting time continuous-spatially discrete response sensitivity equations, are clearly distinguished. The discontinuities in time of the response sensitivities arising due to material state transitions in the plasticity models, and their propagation from the quadrature point level to the global structural response level are discussed using a specific one-dimensional plasticity model. The procedure to obtain the exact sensitivities of the numerical nonlinear finite-element response, including proper capture of their discontinuities, is formalized. Application examples illustrating the concepts are presented at the end.

Finite Element Response Sensitivity Analysis of Steel-Concrete Composite Beams with Deformable Shear Connection

“…Careful examination of the results revealed that no discontinuities occurred exactly at unloading events. This is consistent with prior results on simpler benchmark problems (Conte et al 2003).…”

“…(2) with respect to θ using the chain rule of differentiation (recognizing the explicit and implicit dependence of R on θ), the following response sensitivity equation at the structure level is obtained (Conte et al 2003):…”

“…This is the well-known bilinear inelastic material constitutive model. Detailed formulation and differentiation of this model can be found in (Conte et al 2003). The parameters of this material model consist of (1) Young's modulus of elasticity E, (2) the initial yield stress f y , (3) the linear kinematic hardening modulus H k , and (4) the linear isotropic hardening modulus H i .…”

“…The monotonic and cyclic responses of these material and resulting finite element models are validated through comparison with experimental test results available in the literature (Ansourian 1981, Bursi andGramola 2000). The finite element response sensitivity analysis is performed following the Direct Differentiation Method (DDM) and validated by means of Forward Finite Difference (FFD) analysis (Conte 2001, Conte et al 2003 in the context of two realistic steel-concrete testbed structures considered in this study. The first benchmark structure consists of a non-symmetric two-span continuous beam subjected to a monotonically increasing concentrated force, while the second benchmark structure is a frame sub-assemblage under cyclic loading.…”

“…Following the Direct Differentiation Method (DDM) (Conte 2001, Conte et al 2003, the consistent finite element response sensitivities are computed at each time step, after convergence is achieved for the response computation.…”