‘FE-Meshfree’ QUAD4 element for free-vibration analysis

The FE-LSPIM QUAD4 element, which was recently introduced for the static analysis, uses new shape functions that combine the meshfree and finite element shape functions so as to synergize the individual strengths of meshfree and finite element methods. As a result, the element inherits the completeness properties of meshfree shape functions and the compatibility properties of finite element shape functions. In this paper, the element is extended to free vibration analysis of two-dimensional solids. Typical benchmark problems are solved to test the efficacy of the element. The results show that the element gives more accurate solution than the peer elements particularly under distorted mesh.