محمود عدالتی

The finite element method is a numerical analysis process. This method is one of the most powerful and valuable solutions that many researchers use to obtain the approximate solution of differential equations. Bending plate is one of the difficult problems that has many uses, especially in structures. The exact solution of bending plate is not possible in the general case. In other words, only some of its special cases can be solved with exact solutions. Despite this, the finite element method can analyze many complex cases of bending plates. However, so far, a finite element that can answer all the needs and complexities of various types of bending plates have not been found. Therefore, currently and in the future, researchers will observe other developments in this field. The MATLAB program was used to calculate the outcomes and outputs of the triangular element with the effect of shear deformation, and the accuracy of the function presented for this element was compared with the results of other researchers. The proposed function is calculated for the triangular bending plate element with 15 nodes and 45 degrees of freedom. Finally, the errors of proposed function with 8x8 gridding under concentrated loading at a steel plate with simple edges and thickness of 100 mm, a concrete slab with clamped edges and thickness of 100 mm, a slab rectangular concrete with clamped edges and a very thick concrete slab with fixed edges and thickness of 300 mm are -8.22%, -4.03%, -7.20% and 5.36%, respectively. The errors for mentioned shape function under uniform load with 8 x 8 gridding are at a steel plate with opposite simple edges and a thickness of 200 mm and a concrete slab with clamped edges and 120mm thickness, 12.79% and 5.06%, respectively. For a rectangular concrete slab with clamped edges and 150 mm thickness, the error is 4.62% and for very thick concrete slab with 300mm thickness and clamped edges, the error is 5.07%. Diagrams of displacement, rotation around x and y axes and convergence of problems are also presented in tables and figures. It should be noted that the proposed shape function for the bending plate element has good convergence and is acceptable.