On a new formulation of thin plate element based on the similarity between plane elasticity and plate bending──-from membrane elements to thin plate elements

A new theory and approach of thin plate element on the basis of the similarity theory between plane elasticity and plate bending has been discussed. Because of using approximation of bending moment functions, the requirement of c 1 continuity of displacement in thin plate elements can be avoided naturally. Thin plate elements can be formulated directly at c 0 continuity level for bending moment functions instead of the Reissner Mindlin's thick plate theory for rotations. The locking problems can also be avoided. The relationship between membrane elements and plate bending elements and an approach to transform membrane elements to plate bending ones are presented systematically. A new effective path is supplied to construct high performance thin plate elements. The thin plate elements, called MPS (Membrane Plate Similarity) elements, correspondent to the membrane CST, LST, Q4 and Q8 elements are given. The degrees of freedom of the MPS thin plate elements are deflection and rotations, They can be used easily in practices. Numerical results show that the MPS thin plate elements have a very high precision compared with other plate elements.