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Dual Reciprocity Hybrid Boundary Node Method For 2-d Elasticity With Body Force

机译：体力二维弹性的双互易混合边界节点方法

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摘要

A boundary-type meshless method named dual reciprocity hybrid boundary node method (DRHBNM) is presented. It can be applied to solve elasticity problems with body force, centrifugal load, or other similar problems. In this method, the solution comprises two parts, i.e., the general solution and the particular solution. The general solution is solved by the hybrid boundary node method (HBNM), and the particular one is obtained by the dual reciprocity method (DRM). This method extends the Kelvin fundamental solution for static elastic problems without body force to non-homogeneous problems with body or inertial forces. A modified variational formulation is applied to form the discrete equations of HBNM. The moving least squares (MLS) are employed to approximate the boundary variables, while the domain variables are interpolated by the classical fundamental solution. The particular solution for the body force is obtained by DRM, and the integration in the domain is interpolated by the radial basis function. The proposed method retains the characteristics of the meshless method. At the same time, it employs the fundamental solution as in the boundary element method (BEM). Therefore, this method has the advantages of both meshless method and BEM. It does not require a 'boundary element mesh', either for the purpose of interpolation of the solution variables, or for the integration of the 'energy'. The points in the domain are used only to interpolate particular solutions by the radial basis function and it is not necessary for the integration and approximation of the solution variables. Finally, the boundary solution variables are interpolated by the independent smooth segment boundary. As special treatments for corners are not required, it can obtain accurate boundary tractions for non-smooth boundaries.rnNumerical examples of 2-D elasticity problems with body force are used to demonstrate the versatility of the method and its fast convergence. The computational results for unknown variables are accurate. Also, the variable parameters have little influence on the results and can be changed in wide ranges. It is shown that the present method is effective and can be widely applied to practical problems.
机译：提出了一种边界型无网格方法，称为双互易混合边界节点法（DRHBNM）。它可以用于解决由体力，离心力或其他类似问题引起的弹性问题。在这种方法中，解决方案包括两部分，即一般解决方案和特定解决方案。通用解决方案是通过混合边界节点方法（HBNM）解决的，而特定解决方案是通过对等互惠方法（DRM）获得的。此方法将没有体力的静态弹性问题的Kelvin基本解决方案扩展到具有体力或惯性力的非均匀问题。应用改进的变分公式来形成HBNM的离散方程。移动最小二乘法（MLS）用于近似边界变量，而域变量通过经典基本解进行插值。体力的特定解是通过DRM获得的，并且域的积分是通过径向基函数进行插值的。所提出的方法保留了无网格方法的特征。同时，它采用了边界元法（BEM）中的基本解决方案。因此，该方法同时具有无网格法和边界元法的优点。出于插值求解变量或集成“能量”的目的，它不需要“边界元网格”。域中的点仅用于通过径向基函数对特定解进行插值，而对解变量的积分和逼近则没有必要。最后，边界解变量通过独立的平滑段边界进行插值。由于不需要对角进行特殊处理，因此可以获取非光滑边界的精确边界牵引力。数值算例利用二维力问题的弹力问题证明了该方法的通用性和快速收敛性。未知变量的计算结果是准确的。同样，可变参数对结果的影响很小，可以在较大范围内进行更改。结果表明，本方法是有效的，可以广泛应用于实际问题。

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