Arbitrary quadrangular finite element for plates with shear deformations

Structural mechanics

An arbitrary quadrangular bending finite element based on a piecewise constant approximation of moments is proposed. The solution is based on the principles of minimum additional energy and possible displacements. The finite element allows you to consider the shear deformation, regardless of the ratio of the plate thickness to its sizes. The effect of locking in the calculation of thin plates is absent. Comparison of the results of the oblique plates calculation, annular and round plates with analytical solutions and calculation results for other programs was done. The comparison shows good accuracy in determining displacements and moments. Crushing the finite elements mesh makes the displacement values tend to exact values from above. To assess the influence of the finite element shape, the square plate calculations were made. To model the square plate, quadrangular elements were used, obtained from rectangular ones by changing the slope of one side. At the same time, the calculating accuracy of the displacements and moments decreased slightly. The proposed finite element is easy to implement. The problem solution did not require a numerical integration or the mapping of the quadrangular region to the rectangular one. The necessary expressions were obtained analytically.