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| 1 | 辛求解体系下功能梯度材料平面梁的完整解析解显示文摘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. | 赵莉 陈伟球 吕朝锋 | 2012 | 应用数学和力学2012，33，10： | 2 |
| 2 | Two-dimensional complete rational analysis of functionally graded beams within symplectic framework显示文摘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. | 赵莉 陈伟球 吕朝锋 | 2012 | Applied Mathematics and Mechanics(English Edition)2012，33，10： | 0 |
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