横观各向同性弹性力学空间轴对称问题的复变函数解法
  • 【摘要】

    A transversely isotropic elastic problem is one of the simplest and the most useful anisotropic elastic problems, and develops rapidly in recent years. This paper analyzes present conditions and resea... 展开>>A transversely isotropic elastic problem is one of the simplest and the most useful anisotropic elastic problems, and develops rapidly in recent years. This paper analyzes present conditions and research methods of a transversely isotropic elastic problem for the first time, mean while points out that simpler method can be founded to solve ax symmetric problems. From the fundamental equations of three-dimensional elasticity, the general solution of a transversely isotropic ax symmetric elastic problem is deduced. By means of analytic function and generalized analytic function, this paper proves that choosing two generalized analytic functions of complex function can represent the general solution. By the relation of generalized analytic function and analytic function, generalized analytic functions can be defined by selecting suitable analytic functions, which satisfy the boundary conditions. Expressing the components of stresses displacements and boundary conditions, in the generalized analytic functions defined, the exact solution of a transversely isotropic ax symmetric elastic problem is obtained. To present the feasibility of the method here and to exam the truth of the formulas founded in the paper, using power series solves the problem of a cone pressed at the point, and the result is the same as that solved by other methods. In the end, the problem of circular shaft with globular cavity pressed on the side and pulled on the ends is solved. The method in this paper is valuable when it is investigated deeply. For example, the unite expression of the general solution of the problem of transversely isotropic and isotropic can be seek with complex function. Expending the generalized analytic function with other forms can solve some ax symmetric problems with other figures. 收起<<

  • 【作者】

    王彬 

  • 【学科专业】

    工程力学

  • 【授予学位】

    硕士

  • 【授予单位】

    武汉大学

  • 【导师姓名】

    曾又林

  • 【学位年度】

    2001

  • 【语种】

    chi