Free vibration analysis of thin-walled folded structures employing Galerkin-based RKPM and stabilized nodal integration methods

Abstract

A Galerkin-based meshfree flat shell formulation is chosen to study natural frequency and eigenmode of thin-walled folded structures. Reproducing kernel is used as the interpolation function. Stabilized conforming nodal integration is employed for numerical integration of the weak form. Additionally, sub-domain stabilized conforming integration is adopted for the folded region to integrate the stiffness matrix accurately. The first order shear deformation theory is utilized considering in-plane deformation, out-of-plane deformation and drilling components. The singular kernel function is introduced to effectively handle the folded geometry. An advanced free vibration simulation can be achieved. Accuracy and effectiveness of the meshfree modeling are demonstrated through the numerical examples.