| Meshfree (Mfree) strong method is gradually improving in recent years. Numerical calculation method is purely mesh-free method, without using any grid for Integral. Boundary Element Method is based on the theory of the integral equations, only in the border above partition unit, actually reducing the dimension of the problem. Combining strong meshfree method and Boundary Element Method, bringing the displacement potential function, it may be solved equilibrium equations which based on the elastic theory. Then substituting the boundary equations into the general solution of potential function, it can be determined the unknown parameters and obtained the potential function. It was gain a concrete expression of analytical solution for a gravity wharf. By introduced relevant parameter conditions, it was calculated the maximum displacement. The main results is as follows:(1) It was deduced the displacement potential function under the general solution of expression and derived the control conditions of the parameters.(2) By using quaternions theory and transforming the control differential equation, it was given the general solution of quarternions in domain. According to boundary surface conditions, it was indentificated the parameters of the general solution, which set a new way for solving three-dimensional space problem.(3) By means of two-dimensional meshless strong solution,it was calculated the displacement of a gravity wharf that is 18.7 meters high, and compared with the results by finite element method and norms. In three calculation methods, the results are very close, but much closer to meshless strong method and finite element method.(4) In another apply of meshless strong solution, it was simplified the expressions of the analytical solution in thing plate bending. It was calculate the deflection of the control points through the boundary collocation method. compared with the results by finite element method and norm calculated, they are very close. |
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