The problem of the curved bar subjected to an arbitrarily distributed loading on the surfaces r=a and r=b is sp!ved by using the method of complex functions and expanding the boundary conditions at r=a and r=b into Fo...The problem of the curved bar subjected to an arbitrarily distributed loading on the surfaces r=a and r=b is sp!ved by using the method of complex functions and expanding the boundary conditions at r=a and r=b into Fourier series. Then another paradox in the two-dimensional theory of elasticity is discovered, i. e., the classical solution becomes infinite when the curved bat is subjected to a uniform loading or when the angle included between the two ends of the curved bar 2 alpha is equal to 2 pi and the curved bar is subjected to a sine or cosine loading. In this paper the paradox is resolved successfully and the solutions for the paradox ate obtained. Moreover, the modified classical solution which remains bounded as 2 alpha approaches 2 pi is provided.展开更多
Three displacement functions are introduced to represent each mechanical displacement according to the 3-D theory in this paper. By expanding the displacement functions and the electric potential in orthogonal series,...Three displacement functions are introduced to represent each mechanical displacement according to the 3-D theory in this paper. By expanding the displacement functions and the electric potential in orthogonal series, the free vibration equation of piezoelectric cylindrical shells satisfying SS3 boundary conditions can be obtained. The equation was solved by utilizing Bessel functions with complex arguments. Results are presented graphically as well as in table, and compared with those of other references. Some frequencies that were missing in Ref. [9] are discovered.展开更多
By virtue of the general solution of dynamic elasticity equations for transverse isotropy as well as the variable separation method, three-dimensional exact solutions of circular plates are obtained under two types of...By virtue of the general solution of dynamic elasticity equations for transverse isotropy as well as the variable separation method, three-dimensional exact solutions of circular plates are obtained under two types of boundary conditions. The solutions can consider both axisymmetric and non-axisymmetric cases. Solutions based on the classical plate theory and Mindlin plate theory are also presented under the corresponding boundary conditions. Numerical results are finally presented and comparisons between the three theories are made.展开更多
In this paper a stochastic boundary element method (SEEM) is developed to analyze moderately thick plates with random material parameters and random thickness. Based on the Taylor series expansion, the boundary integr...In this paper a stochastic boundary element method (SEEM) is developed to analyze moderately thick plates with random material parameters and random thickness. Based on the Taylor series expansion, the boundary integration equations concerning the mean and deviation of the generalized displacements are derived, respectively. It is found that the randomness of material parameters is equivalent to a random load, so the mean and covariance matrices of unknown generalized boundary displacements and tractions can be obtained. Furthermore, the mean and covariance of generalized displacements and forces at internal points can also be obtained. A numerical example has been worked out with the method proposed and necessary analysis is made for the results.展开更多
Non-dimensionalized equations and boundary conditions are presented for the torsion problem of an anisotropic body. The error of the fundamental solution cited in some boundary element books Is pointed out after an ex...Non-dimensionalized equations and boundary conditions are presented for the torsion problem of an anisotropic body. The error of the fundamental solution cited in some boundary element books Is pointed out after an examination of the fundamental solution. Furthermore,a necessary and sufficient boundary integral equation is given for the problem and compared with the conventional boundary integral equation. Numerical results show that great errors of the boundary shear stresses obtained by the conventional boundary integral equation appear with a small error of torsion stiffness. Meanwhile,the necessary and sufficient;boundary integral equation always gives accurate results.展开更多
文摘The problem of the curved bar subjected to an arbitrarily distributed loading on the surfaces r=a and r=b is sp!ved by using the method of complex functions and expanding the boundary conditions at r=a and r=b into Fourier series. Then another paradox in the two-dimensional theory of elasticity is discovered, i. e., the classical solution becomes infinite when the curved bat is subjected to a uniform loading or when the angle included between the two ends of the curved bar 2 alpha is equal to 2 pi and the curved bar is subjected to a sine or cosine loading. In this paper the paradox is resolved successfully and the solutions for the paradox ate obtained. Moreover, the modified classical solution which remains bounded as 2 alpha approaches 2 pi is provided.
基金The project is supported by National Natural Science Foundation of ChinaZhejiang Provincial Natural Science Foundation of China.
文摘Three displacement functions are introduced to represent each mechanical displacement according to the 3-D theory in this paper. By expanding the displacement functions and the electric potential in orthogonal series, the free vibration equation of piezoelectric cylindrical shells satisfying SS3 boundary conditions can be obtained. The equation was solved by utilizing Bessel functions with complex arguments. Results are presented graphically as well as in table, and compared with those of other references. Some frequencies that were missing in Ref. [9] are discovered.
基金the National Natural Science Foundation of China(No.19872060)
文摘By virtue of the general solution of dynamic elasticity equations for transverse isotropy as well as the variable separation method, three-dimensional exact solutions of circular plates are obtained under two types of boundary conditions. The solutions can consider both axisymmetric and non-axisymmetric cases. Solutions based on the classical plate theory and Mindlin plate theory are also presented under the corresponding boundary conditions. Numerical results are finally presented and comparisons between the three theories are made.
文摘In this paper a stochastic boundary element method (SEEM) is developed to analyze moderately thick plates with random material parameters and random thickness. Based on the Taylor series expansion, the boundary integration equations concerning the mean and deviation of the generalized displacements are derived, respectively. It is found that the randomness of material parameters is equivalent to a random load, so the mean and covariance matrices of unknown generalized boundary displacements and tractions can be obtained. Furthermore, the mean and covariance of generalized displacements and forces at internal points can also be obtained. A numerical example has been worked out with the method proposed and necessary analysis is made for the results.
文摘Non-dimensionalized equations and boundary conditions are presented for the torsion problem of an anisotropic body. The error of the fundamental solution cited in some boundary element books Is pointed out after an examination of the fundamental solution. Furthermore,a necessary and sufficient boundary integral equation is given for the problem and compared with the conventional boundary integral equation. Numerical results show that great errors of the boundary shear stresses obtained by the conventional boundary integral equation appear with a small error of torsion stiffness. Meanwhile,the necessary and sufficient;boundary integral equation always gives accurate results.
