engleski

Full clamping functions on quadrilateral plate elements

This paper presents a procedure for obtaining an improved finite element solution on quadrilateral plate element. The procedure is performed by estimating the principle of exact displacement method in the finite element technique. The plate elements with three degrees of freedom independent of one another are used, one translational displacement perpendicular to the plate mid-plane and two rotational angles around the two orthogonal axes located at the plate mid-plane. The displacement field of plate element is approximated by two types of functions: the shape functions and full clamping functions. The shape functions satisfy the homogeneous differential equilibrium equation. The full clamping element functions satisfy the full clamping state at the element. The full clamping state at the nodes is satisfied by the selection of the element functions between the functions with full fixed displacements at all finite element nodes. The full clamping functions are taken as an approximation of the deflection surface between a class of functions satisfying the particular solution of the plate bending differential equation between the nodes for determined load. The shape functions are orthogonal with the full clamping functions, therefore, an improved numerical solution is obtained without an increase of the global basis. A number of the full clamping functions depends on a number of different loads on the element. The contribution of introducing the full clamping element functions on plate finite elements is demonstrated in the solution procedure of simply supported plate. An improved numerical solution at the finite element nodes and over the whole finite element is obtained. The accuracy of the solution inside the finite elements is of the same order as at the nodes.

finite element analysis; displacement method; shape functions; full clamping functions

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