Macierz sztywności elementu zginanej płyty trójwarstwowej

Two different methods are used to derive the general expression for the stiffness matrix of an element of a three-layer sandwich plate satisfying N.J. Hoff's [1] assumptions. Dividing the region of the plate into elements and approximating the element displacements by expressions (2.15)-(2.17), an approximate equilibrium equation (3.1)-(3.3) is obtained, and the potential energy functional (2.4) is expressed in terms of the unknown nodal parameters (generalized displacements of the nodes). The matrix of coefficients at the unknowns is the element stiffness matrix required. Using the principle of minimum of the potential energy functional of elastic deformation, an identical expression may be obtained. Eq. (3.23) may also be used to prepare the EMC procedures for particular elements As an example, one term of the stiffness matrix is evaluated for the case of a rectangular element with five degrees of freedom at each node.