Showing papers by "J. N. Reddy published in 1977"

Mixed Rectangular Finite Elements for Plate Bending

Abstract: The paper describes three different rectangular plate bending elements based on Reissner's type stationary variational principles. They differ in the number of dependent variables approximated independently and also in the number of nodes per element. The first element types treats the transverse deflection and the three moments as unknowns at each of the corner nodes; the second element type treats the transverse deflection and two normal moments as unknowns at the corner nodes; the third one treats the transverse deflection as unknown at the corner node, and the moments mx and my at the midnodes of opposite sides of the rectangle. These three types of elements are used to solve square plate problems with various boundary conditions and loadings.

Existence and uniqueness of solutions to a stationary finite element model of the biharmonic equation

Abstract: This paper describes the finite element approximations based on a stationary variational principle of the biharmonic equation. Independent approximations for the solution and its second derivatives are used in the element: the normal derivatives of the solution and its second derivatives are approximated independently on the element boundary. Thus, the present model is a ‘mixed-hybrid’ model. Existence and uniqueness of solutions to the exact weak (or variational) problem are established and the associated finite element approximations are described. Existence and uniqueness of the finite element solutions are proved and a priori error estimates are given.