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首页> 外文期刊>Engineering analysis with boundary elements >Boundary element analysis of 3D cracks in anisotropic thermomagnetoelectroelastic solids
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Boundary element analysis of 3D cracks in anisotropic thermomagnetoelectroelastic solids

机译：各向异性热磁电弹性固体中3D裂纹的边界元分析

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The paper presents a general boundary element approach for analysis of 3D cracks in anisotropic thermomagnetoelectroelastic solids. Dual boundary integral equations are derived, which kernels are explicitly written. These equations do not contain volume integrals in the absence of distributed body heat and extended body forces, which is advantageous comparing to the existing approaches. The issues on the boundary element solution of these equations are discussed in details. The efficient numerical evaluation of kernels based on the trapezoid rule is proposed. Modified Kurt's quadrature with Chebyshev nodes is derived for integration of singular and hypersingular integrals. Nonlinear polynomial mappings are adopted for smoothing the integrand at the crack front, which is advantageous for accurate evaluation of field intensity factors. Special shape functions are introduced, which account for a square-root singularity of extended stress and heat flux at the crack front. The issues on numerical determination of field intensity factors are discussed. Several numerical examples are presented, which show the efficiency (low computational time and high precision) of the proposed boundary element formulation.
机译：本文提出了一种用于分析各向异性热磁电弹性固体中3D裂纹的通用边界元方法。推导了双重边界积分方程，明确地编写了内核。在没有分布的体热和扩展的体力的情况下，这些方程不包含体积积分，这与现有方法相比是有利的。详细讨论了这些方程的边界元解的问题。提出了基于梯形法则的有效数值核估计方法。推导带有Chebyshev节点的经过修改的Kurt正交，用于积分奇异积分和超奇异积分。采用非线性多项式映射来平滑裂纹前沿处的被积物，这有利于准确评估场强因子。引入了特殊的形状函数，这些函数解释了裂纹前沿的扩展应力和热通量的平方根奇异性。讨论了有关场强因子数值确定的问题。给出了几个数值示例，显示了所提出的边界元素公式的效率（低计算时间和高精度）。

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