Elasticity solution of clamped-simply supported beams with variable thickness |
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Authors: | Ye-peng Xu Ding Zhou Y K Cheung |
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Institution: | 1. School of Science,Nanjing University of Science and Technology,Nanjing 210094,P.R.China 2. College of Civil Engineering,Nanjing University of Technology,Nanjing 210009,P.R.China 3. Department of Civil Engineering,Faculty of Engineering,The University of Hong Kong,Hong Kong,P.R.China |
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Abstract: | This paper studies the stress and displacement distributions of continuously varying thickness beams with one end clamped and the other end simply supported under static loads.By introducing the unit pulse functions and Dirac functions,the clamped edge can be made equivalent to the simply supported one by adding the unknown horizontal reactions.According to the governing equations of the plane stress problem,the general expressions of displacements,which satisfy the governing differential equations and the boundary conditions at two ends of the beam,can be deduced.The unknown coefficients in the general expressions are then determined by using Fourier sinusoidal series expansion along the upper and lower boundaries of the beams and using the condition of zero displacements at the clamped edge.The solution obtained has excellent convergence properties.Comparing the numerical results to those obtained from the commercial software ANSYS,excellent accuracy of the present method is demonstrated. |
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Keywords: | beam clamped edge variable thickness Fourier expansion elasticity solution |
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