Using the Green function, the boundary integral formula and natural boundary integral equation for thermal elastic problems are obtained. Then based on bending solutions to circular plates subjected to the non-axi- sy...Using the Green function, the boundary integral formula and natural boundary integral equation for thermal elastic problems are obtained. Then based on bending solutions to circular plates subjected to the non-axi- symmetrical load, by utilizing the Fourier series and convolution formulae, the bending solutions under non-axisymmetrical thermal conditions have been obtained. The calculating process is simple. Examples show the discussed methods are effective.展开更多
Based on the theories of three-dimensional elasticity and piezoelectricity, and by assuming appropriate boundary functions, we established a state equation of piezoelectric cylindrical shells. By using the transfer ma...Based on the theories of three-dimensional elasticity and piezoelectricity, and by assuming appropriate boundary functions, we established a state equation of piezoelectric cylindrical shells. By using the transfer matrix method, we presented an analytical solution that satisfies all the arbitrary boundary conditions at boundary edges, as well as on upper and bottom surfaces. Our solution takes into account all the independent elastic and piezoelectric constants for a piezoelectric orthotropy, and satisfies continuity conditions between plies of the laminates. The principle of the present method and corresponding results can be widely used in many engineering fields and be applied to assess the effectiveness of various approximate and numerical models.展开更多
For non-asymmetrical bending problems of elastic annular plates, the exact solutions are not fond. To bending problems of infinite annular plate with two different boundary conditions, based on the boundary integral f...For non-asymmetrical bending problems of elastic annular plates, the exact solutions are not fond. To bending problems of infinite annular plate with two different boundary conditions, based on the boundary integral formula,the natural boundary integral equation for the boundary value problems of the biharmonic equation and the condition of bending moment in infinity,bending solutions under non-symmetrical loads are gained by the Fourier series and convolution formulae. The formula for the solutions has nicer convergence velocity and high computational accuracy, and the calculating process is simpler. Solutions of the given examples are compared with the finite element method. The textual solutions of moments near the loads are better than the finite element method to the fact that near the concentrative loads the inners forces trend to infinite.展开更多
The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi...The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi_harmonic operator and Laplace operator, applying the multiple reciprocity method(MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high_order fundamental solution sequences.展开更多
Based upon the fundamental equations of three dimensional elasticity, the state equation for axisymmetric bending of laminated transversely isotropic circular plate is established and the concentrated force on plate s...Based upon the fundamental equations of three dimensional elasticity, the state equation for axisymmetric bending of laminated transversely isotropic circular plate is established and the concentrated force on plate surface is expanded into Fourier_Bessel's series, therefore, an analytical solution for the problem is presented. Every fundamental equation of three dimensional elasticity can be exactly satisfied by the solution and all the independent elastic constants can be taken into account fully, furthermore, the continuity conditions between plies can also be satisfied.展开更多
文摘Using the Green function, the boundary integral formula and natural boundary integral equation for thermal elastic problems are obtained. Then based on bending solutions to circular plates subjected to the non-axi- symmetrical load, by utilizing the Fourier series and convolution formulae, the bending solutions under non-axisymmetrical thermal conditions have been obtained. The calculating process is simple. Examples show the discussed methods are effective.
基金Funded by the Natural Science Foundation of Anhui Province (No. 070414190)
文摘Based on the theories of three-dimensional elasticity and piezoelectricity, and by assuming appropriate boundary functions, we established a state equation of piezoelectric cylindrical shells. By using the transfer matrix method, we presented an analytical solution that satisfies all the arbitrary boundary conditions at boundary edges, as well as on upper and bottom surfaces. Our solution takes into account all the independent elastic and piezoelectric constants for a piezoelectric orthotropy, and satisfies continuity conditions between plies of the laminates. The principle of the present method and corresponding results can be widely used in many engineering fields and be applied to assess the effectiveness of various approximate and numerical models.
基金Project supported by the National Basic Research Program of China (No. 2007CB209400)the National Nature Fond (No. 50774077 and 50774081)the National Fond of Author of Doctor Thesis (100760)
文摘For non-asymmetrical bending problems of elastic annular plates, the exact solutions are not fond. To bending problems of infinite annular plate with two different boundary conditions, based on the boundary integral formula,the natural boundary integral equation for the boundary value problems of the biharmonic equation and the condition of bending moment in infinity,bending solutions under non-symmetrical loads are gained by the Fourier series and convolution formulae. The formula for the solutions has nicer convergence velocity and high computational accuracy, and the calculating process is simpler. Solutions of the given examples are compared with the finite element method. The textual solutions of moments near the loads are better than the finite element method to the fact that near the concentrative loads the inners forces trend to infinite.
文摘The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi_harmonic operator and Laplace operator, applying the multiple reciprocity method(MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high_order fundamental solution sequences.
文摘Based upon the fundamental equations of three dimensional elasticity, the state equation for axisymmetric bending of laminated transversely isotropic circular plate is established and the concentrated force on plate surface is expanded into Fourier_Bessel's series, therefore, an analytical solution for the problem is presented. Every fundamental equation of three dimensional elasticity can be exactly satisfied by the solution and all the independent elastic constants can be taken into account fully, furthermore, the continuity conditions between plies can also be satisfied.
