A Generalized Coordinated Rectangle Element for Thick and Thin Plate
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The structure coordination and shear unlocking middle thick plate element is a problem to which people pay close attention in the finite element analysis of plate.A supposed shear strain field is presented in the documents [2,3] and a generalized triangle and quadrangle element for thick and thin plates is developed by generalized coordination theory.But this kind of element is not perfect and harmonized in deed.Therefore,a coordinating and harmonized rectangle elements for thin plate is constructed in the document [1] ,and it provides a new valid way for constructing this kind of element. Firstly,the variation function of shear strain along each side and at node of the element are determined based on the Mindin thick plate theory,and the shear strain fields in the domain of the element are detemined with improved interpolation in this paper.When thickness of plate become small,the thick theory is automatically degenerated the thin theory,and shear strain along each side of element and the variation function of shear strain of element are automatically shear locking.Secondly,based on the relation of the rotation,flexivity and strain fields in the domain of the elements,a generalized coordinating twelve freedom rectangle element for thick and thin plates is developed by repeated trying.It is proved by theory that the elements are perfect,harmonized and free of shear locking.The C repeated continuity and shear locking problem of element for thick and thin plate is solved preferably. In order to validate the correctness of the coordinating element,center flexivity and bending moments of square plate are analyzed in this paper and the plate is supported simply and fixed at four sides in different ratio of thickness to span and is acted on equispared load.The convergence velocity of the calculated result by this coordinating plate element is faster and the precision is higher than the average,and the principle and formula is more simple,and the freedom degree of the element is fewer.The element is degenerated coordinating thin plate element and is free of shear locking in the case of thin plate.The result calculated by the coordinating element is very near to that of Mindin middle thick plates in the case of near to thick plate,and the coordinating element can be used to different thickness plates and is a fine element.