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采用辛弹性力学解法,求取弹性模量沿轴向指数变化,而Poisson比保持不变的功能梯度材料平面梁的完整解析解.通过求解被Saint-Venant原理覆盖的一般本征解,建立起完整的解析分析过程,进而给出平面梁位移和应力的精确分布规律.传统的弹性力学分析方法常常忽略被Saint-Venant原理覆盖的解,但这些衰减的本征解对材料的局部效应起着较大的影响作用,可能导致材料或结构的突然失效.采用辛求解方法,充分利用本征向量之间的辛共轭正交关系,得到了功能梯度材料梁的完整解析解.两个数值算例分别将功能梯度材料平面梁的位移和应力分布与相应均匀材料情形的结果进行比较,研究了材料非均匀性对位移和应力解的影响. 相似文献
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Exact solutions for generally supported functionally graded plane beams are given within the framework of symplectic elasticity. The Young’s modulus is assumed to exponentially vary along the longitudinal direction while the Poisson’s ratio remains constant. The state equation with a shift-Hamiltonian operator matrix has been established in the previous work, which is limited to the Saint-Venant solution. Here, a complete rational analysis of the displacement and stress distributions in the beam is presented by exploring the eigensolutions that are usually covered up by the Saint-Venant principle. These solutions play a significant role in the local behavior of materials that is usually ignored in the conventional elasticity methods but possibly crucial to the material/structure failures. The analysis makes full use of the symplectic orthogonality of the eigensolutions. Two illustrative examples are presented to compare the displacement and stress results with those for homogenous materials, demonstrating the effects of material inhomogeneity. 相似文献
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第二届亚洲功能材料与结构力学大会于2010年10月22~25日在南京航空航天大学成功举行.本届大会由中国力学学会和江苏省力学学会主办、南京航空航天大学承办.会议延续在日本Matsue召开首届大会的目的:旨为亚洲及其周边地区从事功能材料与结构力学的科研工作者提供一个交流的平台,共同促进该领域在理论与应用方面的发展. 相似文献
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The plate theory of functionally graded materials suggested by Mian and Spencer is extended to analyze the cylindrical bending problem of a functionally graded rectangular plate subject to uniform load. The expansion formula for displacements is adopted. While keeping the assumption that the material parameters can vary along the thickness direction in an arbitrary fashion, this paper considers orthotropic materials rather than isotropic materials. In addition, the traction-free condition on the top surface is replaced with the condition of uniform load applied on the top surface. The plate theory for the particular case Of cylindrical bending is presented by considering an infinite extent in the y-direction. Effects of boundary conditions and material inhomogeneity on the static response of functionally graded plates are investigated through a numerical example. 相似文献
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The elastodynamic problems of piezoelectric hollow cylinders and spheres under radial deformation can be transformed into a second kind Volterra integral equation about a function with respect to time, which greatly simplifies the solving procedure for such elastodynamic problems. Meanwhile, it becomes very important to find a way to solve the second kind Volterra integral equation effectively and quickly. By using an interpolation function to approximate the unknown function, two new recursive formulae were derived, based on which numerical solution can be obtained step by step. The present method can provide accurate numerical results efficiently. It is also very stable for long time calculating. 相似文献
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For the thermoelastic dynamic axisymmetric problem of a finite orthotropic hollow cylinder, one comes closer to reality to
involve the effect of axial strain than to consider the plane strain case only. However, additional mathematical difficulties
should be encountered and a different solution procedure should be developed. By the separation of variables, the thermoelastic
axisymmetric dynamic problem of an orthotropic hollow cylinder taking account of the axial strain is transformed to a Volterra
integral equation of the second kind for a function of time, which can be solved efficiently and quickly by the interpolation
method. The solutions of displacements and stresses are obtained. It is noted that the present method is suitable for an orthotropic
hollow cylinder with an arbitrary thickness subjected to arbitrary axisymmetric thermal loads. Numerical comparison is made
to show the effect of the axial strain on the displacements and stresses.
The project supported by the National Natural Science Foundation of China (10172075) and China Postdoctoral Science Foundation
(20040350712) 相似文献
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