Analysis and optimization of dynamically loaded reinforced plates by the coupled boundary and finite element method

The aim of the present work is to analyze and optimize plates in plane strain or stress with stiffeners subjected to dynamic loads. The reinforced structures are analyzed using the coupled boundary and finite element method. The plates are modeled using the. dual reciprocity boundary element method (DR-BEM) and the stiffeners using the finite element method (FEM). The matrix equations of motion are formulated for the plate and stiffeners. The equations are coupled using conditions of compatibility of displacements and equilibrium of tractions along the interfaces between the plate and stiffeners. The final set of equations of motion is solved step-by-step using the Houbolt direct integration method. The direct solutions are displacements and tractions for boundary and interface nodes in each time step. The aim of optimization is to find the optimal lengths and locations of stiffeners. The objective functions, which characterize strength and stiffness, depend on displacements or tractions. The optimization problem is solved using an evolutionary method. The results of the dynamic analysis by the proposed method are compared with the solutions computed by the professional finite element code, showing a very good agreement. As the result of optimization, an improvement of dynamic response is obtained, in comparison with an initial design.