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Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally. [ABSTRACT FROM AUTHOR]

An exact analytical solution was presented for free vibration of composite shell structure-hermetic capsule. The basic equations on axisymmetric vibration were based on the Love classical thin shell theory and derived for shells of revolution with arbitrary meridian shape. The conditions of the junction between the spherical and the cylindrical shell segments are given by the continuity of deformation and the equilibrium relations near the junction point. The mathematical model of problem is reduced to as an eigenvalue problem for a system of ordinary differential equations in two separate domains corresponding to the spherical and the cylindrical shell segments. By using Legendre and trigonometric functions, exact and explicitly analytical solutions of the mode functions were constructed and the exact frequency equation were obtained. The implementation of Maple programme indicates that all calculations are simple and efficient in both the exact symbolic calculation and the numerical results of natural frequencies compare with the results using finite element methods and other numerical methods. As a benchmark, the exactly analytical solutions presented in this paper is valuable to examine the accuracy of various approximate methods. [ABSTRACT FROM AUTHOR]

An exact analytical solution was presented for free vibration of composite shell structure-hermetic capsule. The basic equations on axisymmetric vibration were based on the Love classical thin shell theory and derived for shells of revolution with arbitrary meridian shape. The conditions of the junction between the spherical and the cylindrical shell segments are given by the continuity of deformation and the equilibrium relations near the junction point. The mathematical model of problem is reduced to as an eigenvalue problem for a system of ordinary differential equations in two separate domains corresponding to the spherical and the cylindrical shell segments. By using Legendre and trigonometric functions, exact and explicitly analytical solutions of the mode functions were constructed and the exact frequency equation were obtained. The implementation of Maple programme indicates that all calculations are simple and efficient in both the exact symbolic calculation and the numerical results of natural frequencies compare with the results using finite element methods and other numerical methdos. As a benchmark, the exactly analytical solutions presented in this paper is valuable to examine the accuracy of various approximate methods. [ABSTRACT FROM AUTHOR]