Stress boundary conditions for plate bending |
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| Institution: | 1. Department of Civil Engineering, The British University in Egypt, Cairo, Egypt;2. CUFE-BE Research Group: http://eng.cu.edu.eg/postgraduate-portal/research-groups, Department of Structural Engineering, Cairo University, Giza, Egypt;3. Supreme Council of Universities, Egypt;1. School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China;2. Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Centre for Engineering, Edmonton, Alberta T6G 1H9, Canada;1. Institute of Nuclear Energy Research, No. 1000, Wunhua Road, Jiaan Village, Lungtan, Township, Taoyuan County 32546, Taiwan;2. Department of Mechanical Engineering, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 106, Taiwan;1. School of Transportation Science and Engineering, Beihang University, Beijing 100191, China;2. National Institute of Metrology, Beijing 100023, China;1. School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, People’s Republic of China;2. The Key Laboratory for Special Fiber and Fiber Sensor of Hebei Province, People’s Republic of China |
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| Abstract: | The determination of the appropriate boundary conditions for a two-dimensional theory of elastic flat plates (and shells) consistent with the expected order of accuracy of the theory is both critical and challenging. The reciprocal theorem of elasticity will be applied in a novel way to obtain the appropriate stress boundary conditions for plate bending accurate to all order (with respect to the usual dimensionless thickness parameter) for plates of general edge geometry and loading. Kirchhoff’s two contracted stress boundary conditions are shown to be consistent with a leading term (thin plate) approximation theory, but the more general results obtained herein are needed for higher order theories. |
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