Abstract
A new method is used to solve the rectangular plate bending problem with mixed boundary conditions. The method overcomes the complicated derivation of the classical solution by Fourth-order differential problem into integrating question. Under uniform loading rectangular plate bending problem with one side fixed the opposite side half simply supported half fixed the other two sides free rectangular plate, one side simply supported the opposite side half simply supported half fixed the other two sides free rectangular plate is systematically solved. According to the actual boundary conditions of the rectangular plate, the corresponding characteristic equation can easily be set up. It is presented deflection curve equation and the numerical calculation. By compared the results of the equation to the finite element program, we are able to demonstrate the correctness of the method. So the method not only has certain theoretical value, but also can be directly applied to engineering practice.
Highlights
With the development of the construction industry, the diversity of building is in high demand
The method is no need to consider the hypothesis of complex displacement function, which can be very easy to write the total potential energy of rectangular plate on mixed boundary conditions
Mixed total potential energy is required that the displacement is weakly allowed and the boundary force is coordination allowed [9]
Summary
With the development of the construction industry, the diversity of building is in high demand. It is more and more important to calculate plates under various constraint conditions. The method is no need to consider the hypothesis of complex displacement function, which can be very easy to write the total potential energy of rectangular plate on mixed boundary conditions. According to the actual boundary conditions of rectangular plate, corresponding characteristic equation can be established, thereby to overcome the cumbersome derivation process in classic solution. Because this method is simple and program characteristics, especially which is more efficient to solve the other methods are not easy to solve problems
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