We investigate (i) pull-in instabilities in a microelectromechanical (MEM) beam due to the Coulomb force and in MEM membranes due to the Coulomb and the Casimir forces, and (ii) thermomechanical instability in a heat-conducting thermoelastoviscoplastic solid due to thermal softening overcoming hardening caused by strain- and strain-rate effects. Each of these nonlinear multiphysics problems is analyzed by the meshless local Petrov-Galerkin (MLPG) method. The moving least squares (MLS) approximation is used to generate basis functions for the trial solution, and the basis for test functions is taken to be either the weight functions used in the MLS approximation, or the same as for the trial solution. In this case the method becomes Bubnov-Galerkin. Essential (displacement, temperature, electric potential) boundary conditions are enforced by the method of Lagrange multipliers. For the electromechanical problem, the pull-in voltage and the corresponding deflection are extracted by combining the MLPG method with either the displacement iteration pull-in extraction algorithm or the pseudoarclength continuation method. For the thermomechanical problem, the localization of deformation into narrow regions of intense plastic deformation is delineated. For every problem studied, computed results are found to compare well with those obtained either analytically or by the finite element (FE) method. For the same accuracy, the MLPG method generally requires fewer nodes but more CPU time than the FE method; thus additional computational cost is compensated somewhat by the increased efficiency of the MLPG method. / Ph. D.

Transparent laminates are widely used for body armor, goggles, windows and windshields. Improved understanding of their deformations under impact loading and of energy dissipation mechanisms is needed for minimizing their weight. This requires verified and robust computational algorithms and validated mathematical models of the problem. Here we have developed a mathematical model for analyzing the impact response of transparent laminates made of polymeric materials and implemented it in the finite element software LS-DYNA. Materials considered are polymethylmethacrylate (PMMA), polycarbonate (PC) and adhesives. The PMMA and the PC are modeled as elasto-thermo-visco-plastic and adhesives as viscoelastic. Their failure criteria are stated and simulated by the element deletion technique. Values of material parameters of the PMMA and the PC are taken from the literature, and those of adhesives determined from their test data. Constitutive equations are implemented as user-defined subroutines in LS-DYNA which are verified by comparing numerical and analytical solutions of several initial-boundary-value problems. Delamination at interfaces is simulated by using a bilinear traction separation law and the cohesive zone model. We present mathematical and computational models in chapter one and validate them by comparing their predictions with test findings for impacts of monolithic and laminated plates. The principal source of energy dissipation of impacted PMMA/adhesive/PC laminates is plastic deformations of the PC. In chapter two we analyze impact resistance of doubly curved monolithic PC panels and delineate the effect of curvature on the energy dissipated. It is found that the improved performance of curved panels is due to the decrease in the magnitude of stresses near the center of impact. In chapter three we propose constitutive relations for finite deformations of adhesives and find values of material parameters by considering test data for five portions of cyclic loading. Even though these values give different amounts of energy dissipated in the adhesive, their effect on the computed impact response of PMMA/adhesive/PC laminates is found to be minimal. In chapter four we conduct sensitivity analysis to identify critical parameters that significantly affect the energy dissipated. The genetic algorithm is used to optimally design a transparent laminate in chapter five. / Ph. D.