Abstract
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.
Highlights
Due to the complexity of the thermoelasticity problems, analytic solutions can be obtained only for axisymmetrical problems and problems [1,2,3,4,5,6]
Based on bending solutions to circular plates subjected to the non-axisymmetrical load, by utilizing the Fourier series and convolution formulae, the bending solutions under nonaxisymmetrical thermal conditions have been obtained
The differential equation of elastic plate bending problems is where, is the Laplacian operator, u is the deflection of the plate, q is the surface density of external loads, D is the bending rigidity of the plate, is the plate in a circle domain
Summary
Due to the complexity of the thermoelasticity problems, analytic solutions can be obtained only for axisymmetrical problems and problems [1,2,3,4,5,6]. For general non-axisymmetrical loads and general non-axisymmetrical boundary conditions, the numerical computation is the main method [7,8,9]. For bending problems of solid circular plates, Fu Bao-lian adopted the reciprocal theorem and took the solution of the clamped circular plate as the basic solution to discuss some bending solutions under axis-symmetrical loads [10]. Yu De-hao discussed bending problems of plates with the natural boundary element method [13,14]. Li Shun-cai discussed the bending problems of solid circular plates under the boundary loads [15,16,17]. On the basis of the same method, using Fourier series and several convolution formulae, the boundary integral formula and natural boundary integral equation for the thermal bending of circular plates are obtained.
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