Application of the three-node triangular element with continuous nodal stress for free vibration analysis

A three-node triangular element with continuous nodal stress (Trig3-CNS) was recently proposed for static analysis. The Trig3-CNS element, which is the development of the partition-of-unity based “FE-Meshfree” quadrilateral element with continuous nodal stress (Quad4-CNS), uses hybrid 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, high order global approximations in Trig3-CNS element could be easily constructed without adding extra nodes and DOFs, thereby achieving high accuracy and convergence rate. In this paper, the element is further applied to conduct free vibration analysis of two-dimensional solids. The numerical tests in the present work demonstrate that Trig3-CNS has higher tolerance to mesh distortion and gives more accurate solution as compared to the three-node triangular element (Trig3) and four-node quadrilateral element (Quad4).