In this paper,the dynamic stress concentration and scattering of SH-waves by bi-material structures that possess an interface elliptic cavity are investigated.First,by using the complex function method,the Green's...In this paper,the dynamic stress concentration and scattering of SH-waves by bi-material structures that possess an interface elliptic cavity are investigated.First,by using the complex function method,the Green's function is constructed.This yields the solution of the displacement field for an elastic half space with a semi-elliptic canyon impacted by an anti-plane harmonic line source loading on the horizontal surface.Then,the problem is divided into an upper and lower half space along the horizontal interface,regarded as a harmony model.In order to satisfy the integral continuity condition, the unknown anti-plane forces are applied to the interface.The integral equations with unknown forces can be established through the continuity condition,and after transformation,the algebraic equations are solved numerically.Finally,the distribution of the dynamic stress concentration factor(DSCF)around the elliptic cavity is given and the effect of different parameters on DSCF is discussed.展开更多
Using the method of the boundary integral equation, a set of singular integral equations of the hear transfer problems and the thermo-elastic problems of a crack embedded in a two-dimensional finite body is derived, a...Using the method of the boundary integral equation, a set of singular integral equations of the hear transfer problems and the thermo-elastic problems of a crack embedded in a two-dimensional finite body is derived, and then,its numerical method is proposed by the numerical method of the singular integral equations combined with boundary element method. Moreover, the singular nature of temperature gradient field near the crack front is proved by the main-part analysis method of the singular integral equation, and the singular temperature gradients are exactly obtained. Finally, several typical examples calculated.展开更多
The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an...The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.展开更多
In this study, integral operational methods are used to investigate the thermally induced transverse vibration of a thin elliptic annulus plate with elastic supports at both radial boundaries.The axisymmetric temperat...In this study, integral operational methods are used to investigate the thermally induced transverse vibration of a thin elliptic annulus plate with elastic supports at both radial boundaries.The axisymmetric temperature distribution is determined by the heat conduction differential equation and its corresponding boundary conditions by employing a unified integral transform technique by use of Mathieu functions and modified Mathieu functions. The solution of thermally induced vibration of the plate with both ends encased with elastic supports is obtained by employing an integral transform for double Laplace differential equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained based on resultant bending moments per unit width. The numerical calculations of the distributions of the transient temperature and its associated stress distributions are shown in the figures.展开更多
一体化热防护结构通常处于严酷的非稳态热环境,热载荷作用的时间效应(即瞬态热效应)明显.为了避免瞬态热分析的巨大计算消耗,以往的一体化热防护结构优化设计研究通常将瞬态传热等效为相同热边界条件下的稳态传热,将稳态传热分析的温度...一体化热防护结构通常处于严酷的非稳态热环境,热载荷作用的时间效应(即瞬态热效应)明显.为了避免瞬态热分析的巨大计算消耗,以往的一体化热防护结构优化设计研究通常将瞬态传热等效为相同热边界条件下的稳态传热,将稳态传热分析的温度场作为设计热载荷.然而,已有的研究表明稳态传热无法准确等效瞬态传热的作用效果,瞬态热效应对结构设计结果具有重要影响.文章研究了考虑瞬态热效应的一体化热防护结构优化设计问题,建立一种考虑瞬态温度和应力约束的一体化热防护结构拓扑优化方法.该方法以SIMP(solid isotropic material with penalization)法为基础,构建两种针对一体化热防护结构的热弹性结构拓扑优化模型:(1)考虑材料体积分数、最大应力和底面最大温度约束,以最小化结构应变能为目标的刚度设计模型;(2)考虑最大应力和底面最大温度约束,以最小化材料体积分数为目标的轻量化设计模型.通过求解瞬态热力耦合方程获得结构的热力耦合静力分析结果;通过响应量在空间和时间域的凝聚积分函数表征结构响应在时域内的最大值,并以此构建相应的约束和目标函数;采用伴随法推导约束和目标函数的灵敏度表达式.通过3个数值算例验证了本方法的有效性.数值算例结果表明,在瞬态传热条件下,本方法能够准确反映瞬态热效应对一体化热防护结构设计结果的影响;相比于基于稳态热分析的设计结果,考虑瞬态热效应的设计结果具有更优的性能.展开更多
When concentrated forces are applied at any points of the outer region of an ellipse in an infinite plate, the complex potentials are determined using the conformal mapping method and Cauchy＇s integral formula. And t...When concentrated forces are applied at any points of the outer region of an ellipse in an infinite plate, the complex potentials are determined using the conformal mapping method and Cauchy＇s integral formula. And then, based on the superposition principle, the analyt- ical solutions for stress around an elliptical hole in an infinite plate subjected to a uniform far-field stress and concentrated forces, are obtained. Tangential stress concentration will occur on the hole boundary when only far-field uniform loads are applied. When concen- trated forces are applied in the reversed directions of the uniform loads, tangential stress concentration on the hole boundary can be released significantly. In order to minimize the tangential stress concentration, we need to determine the optimum positions and values of the concentrated forces. Three different optimization methods are applied to achieve this aim. The results show that the tangential stress can be released significantly when the op- timized concentrated forces are applied.展开更多
文摘In this paper,the dynamic stress concentration and scattering of SH-waves by bi-material structures that possess an interface elliptic cavity are investigated.First,by using the complex function method,the Green's function is constructed.This yields the solution of the displacement field for an elastic half space with a semi-elliptic canyon impacted by an anti-plane harmonic line source loading on the horizontal surface.Then,the problem is divided into an upper and lower half space along the horizontal interface,regarded as a harmony model.In order to satisfy the integral continuity condition, the unknown anti-plane forces are applied to the interface.The integral equations with unknown forces can be established through the continuity condition,and after transformation,the algebraic equations are solved numerically.Finally,the distribution of the dynamic stress concentration factor(DSCF)around the elliptic cavity is given and the effect of different parameters on DSCF is discussed.
文摘Using the method of the boundary integral equation, a set of singular integral equations of the hear transfer problems and the thermo-elastic problems of a crack embedded in a two-dimensional finite body is derived, and then,its numerical method is proposed by the numerical method of the singular integral equations combined with boundary element method. Moreover, the singular nature of temperature gradient field near the crack front is proved by the main-part analysis method of the singular integral equation, and the singular temperature gradients are exactly obtained. Finally, several typical examples calculated.
文摘The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.
文摘In this study, integral operational methods are used to investigate the thermally induced transverse vibration of a thin elliptic annulus plate with elastic supports at both radial boundaries.The axisymmetric temperature distribution is determined by the heat conduction differential equation and its corresponding boundary conditions by employing a unified integral transform technique by use of Mathieu functions and modified Mathieu functions. The solution of thermally induced vibration of the plate with both ends encased with elastic supports is obtained by employing an integral transform for double Laplace differential equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained based on resultant bending moments per unit width. The numerical calculations of the distributions of the transient temperature and its associated stress distributions are shown in the figures.
文摘一体化热防护结构通常处于严酷的非稳态热环境,热载荷作用的时间效应(即瞬态热效应)明显.为了避免瞬态热分析的巨大计算消耗,以往的一体化热防护结构优化设计研究通常将瞬态传热等效为相同热边界条件下的稳态传热,将稳态传热分析的温度场作为设计热载荷.然而,已有的研究表明稳态传热无法准确等效瞬态传热的作用效果,瞬态热效应对结构设计结果具有重要影响.文章研究了考虑瞬态热效应的一体化热防护结构优化设计问题,建立一种考虑瞬态温度和应力约束的一体化热防护结构拓扑优化方法.该方法以SIMP(solid isotropic material with penalization)法为基础,构建两种针对一体化热防护结构的热弹性结构拓扑优化模型:(1)考虑材料体积分数、最大应力和底面最大温度约束,以最小化结构应变能为目标的刚度设计模型;(2)考虑最大应力和底面最大温度约束,以最小化材料体积分数为目标的轻量化设计模型.通过求解瞬态热力耦合方程获得结构的热力耦合静力分析结果;通过响应量在空间和时间域的凝聚积分函数表征结构响应在时域内的最大值,并以此构建相应的约束和目标函数;采用伴随法推导约束和目标函数的灵敏度表达式.通过3个数值算例验证了本方法的有效性.数值算例结果表明,在瞬态传热条件下,本方法能够准确反映瞬态热效应对一体化热防护结构设计结果的影响;相比于基于稳态热分析的设计结果,考虑瞬态热效应的设计结果具有更优的性能.
基金supported by the National Natural Science Foundation of China [grant numbers 11172101, 11572126]
文摘When concentrated forces are applied at any points of the outer region of an ellipse in an infinite plate, the complex potentials are determined using the conformal mapping method and Cauchy＇s integral formula. And then, based on the superposition principle, the analyt- ical solutions for stress around an elliptical hole in an infinite plate subjected to a uniform far-field stress and concentrated forces, are obtained. Tangential stress concentration will occur on the hole boundary when only far-field uniform loads are applied. When concen- trated forces are applied in the reversed directions of the uniform loads, tangential stress concentration on the hole boundary can be released significantly. In order to minimize the tangential stress concentration, we need to determine the optimum positions and values of the concentrated forces. Three different optimization methods are applied to achieve this aim. The results show that the tangential stress can be released significantly when the op- timized concentrated forces are applied.
