Handling of Constraints in Finite-Element Response Sensitivity Analysis

In this paper, the direct differentiation method DDM for finite-element FE response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints MPCs . The analytical developments are provided for three different constraint handling methods, namely: 1 the transformation equation method; 2 the Lagrange multiplier method; and 3 the penalty function method. Two nonlinear benchmark applications are presented: 1 a two-dimensional soil-foundation-structure interaction system and 2 a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDMbased response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE responseonly analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating. DOI: 10.1061/ ASCE EM.1943-7889.0000053 CE Database subject headings: Finite element method; Constitutive models; Constraints; Sensitivity analysis; Soil-structure interactions.