First failure load of sandwich beams under transient loading using a space–time coupled finite element method. (April 2022) - Burns, Devin J.; Batra, R.C.
Abstract: We numerically analyze transient plane stress deformations of linearly elastic laminates and sandwich structures by using a coupled space–time finite element method with the weak form of governing equations derived by the least-squares method. The governing equations are written as seven first-order partial differential equations as in the state space formulation, and each variable is approximated by using piece-wise continuous basis functions. The sum of the integral over the problem (space-time) domain of squares of residuals of the governing equations, and initial and boundary conditions is minimized with respect to the nodal values of the seven variables to deduce coupled linear algebraic equations. The developed software is verified by comparing computed results for sample problems with their either analytical or numerical solutions obtained with a commercial software, ABAQUS. Using statistical method and the Tsai–Wu failure criterion, sensitivities of the maximum deflection and the first failure load to beam's aspect ratio (AR), the facesheet-core thickness ratio (FCTR), and the facesheet-core in-plane and transverse stiffness ratios (FCISR, FCTSR) are elucidated. For sandwich beams with equal FCISR and FCTSR, the results are sensitive to the AR and the FCTR. In general, they strongly depend upon the FCTSR and its interaction with the AR and the FCTR. Highlights: Analysis of transient problem using space–time coupled finite element method. Statistical analysis of interaction among various geometric parameters on structure's response. State-space formulation of governing equations to accurately compute transverse stresses.