Using finite element analysis/optimum design in the determination of elastic constants by vibration testing

Abstract

Combining vibration testing and numerical methods is a potential alternative approach for determining elastic constants of materials because of nondestructive testing, single testing, and producing average properties. In order to simplify the modeling processes and to reduce complicated derivations in the numerical method, the combination of finite element analysis and optimum design is adopted in this work to inversely calculate the elastic constants. In this method, the effects of some parameters, including the finite element mesh, the mode number, constraints on state variables, the optimization method, and initial values and loops, are discussed. It is proved that the present method with 10×10 mesh, 6 vibration modes, 5% constraint on state variables, and subproblem approximation can obtain accurate results. Average values can be used to avoid the scatter in results due to different initial values, and do‐loops may not be necessary. It is also clearly demonstrated that the present method can correctly extract 2 or 5 elastic constants for isotropic or orthotropic materials.