Solution of Non-rectangular Plates with Macroelement Method

New approach to static analysis of thin non-rectangular arbitrarily loaded plates, called the macroelement method, has been developed in this paper. Macroelement is a rectangular plate which entirely contains real plate. The mathematical model of macroelement was built. The equilibrium equations are performed for macroelement and boundary conditions are written on the line corresponding to contour of real plate in the nodes which are zero points of trigonometric functions, included in the macroelement model. The load is applied only to separate nodes on the surface of real plate, whereas the complement of a plate to macroelement is unloaded. Analysis of construction is reduced to solving a system of linear algebraic equations. The method provides better accuracy compared to finite element method and requires less equations. There is trapeze plate clamped at inclined edge and simply supported at opposite one considered in this paper. The other edges of the plate are free. Uniformly distributed load on the surface of real plate is taken into account.