HIGH-ORDER HYBRID STRESS TRIANGULAR ELEMENT FOR MINDLIN PLATE BENDING AND VIBRATION ANALYSIS

Current patch test for Mindlin plate element only satisfies the zero shear deformation condition, while the non-zero constant shear condition cannot be satisfied. Based on the Reissner-Mindlin theory, i.e. first-order shear deformable theory and complementary energy principle, a 6-node higher-order hybrid stress triangular element is presented for Mindlin plates to pass both the zero shear patch test and the non-zero constant shear enhanced patch test. For this purpose, special attention is devoted to selecting boundary displacement interpolation and stress approximation in domain. The arbitrary order Timoshenko beam function is used successfully to derive the boundary displacement interpolation. According to the equilibrium equations, an appropriate stress approximation is rationally derived. This paper discusses the application of the proposed element to the bending and free vibration of plates with different boundary conditions and thicknesses, and the lumped mass matrix is adopted. Numerical results show that the element can be used to analyze both moderately thick and thin plates efficiently and accurately.