Development and Verification of Shear Projection Virtual Element

This paper introduces extensions and further verification of the newly developed reduced order shear projection virtual element for Mindlin plates. The construction of the mass matrix and the buckling geometric stiffness matrix are developed and the J-integral for Mindlin plates is implemented. For the first time the Virtual Element Method (VEM) is used to solve the free vibration and buckling problems for Mindlin plates, and to calculate the bending stress intensity factor, K 1B for cracked plates. Numerical tests are performed for all of the problems, and are compared to Finite Element Method (FEM) results, and previously published analytical results. The VEM results agree closely with the FEM and analytical results, with the first natural frequency found with the VEM converging to within 0.4% of the FEM result, and the VEM result of the first buckling load is over 1% more accurate than that from the FEM for thin plates. The value of K 1B calculated by the VEM agrees closely with published results, even on coarse meshes, and those within special consideration of the crack tip.