Modified Mindlin plate theory and shear locking-free finite element formulation |
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| Affiliation: | 1. Faculty of Civil Engineering and Applied Mechanics, University of Technical Education Ho Chi Minh City, 1 Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City, Viet Nam;2. Faculty of Engineering and Environment, Northumbria University, Newcastle Upon Tyne NE1 8ST, UK;3. Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia;1. Faculty of Engineering and Environment, Northumbria University, Newcastle upon Tyne NE1 8ST, UK;2. School of Civil and Environmental Engineering, The University of New South Wales, NSW 2052, Australia;3. Faculty of Civil Engineering and Applied Mechanics, University of Technical Education Ho Chi Minh City, 1 Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City, Viet Nam;4. Department of Architectural Engineering, Sejong University, 98 Kunja Dong, Kwangjin Ku, Seoul 143-747, Republic of Korea;1. Department of Mechanical and Construction Engineering, Northumbria University, Ellison Place, Newcastle upon Tyne NE1 8ST, UK;2. School of Engineering and Mathematical Sciences, La Trobe University, Bundoora, VIC 3086, Australia;3. Faculty of Civil Engineering and Applied Mechanics, University of Technical Education Ho Chi Minh City, 1 Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City, Viet Nam;4. Duy Tan University, Da Nang, Viet Nam;1. Aerospace Engineering Department, Indian Institute of Technology Bombay, Mumbai 400076 India;2. Mechanical Engineering Department, Indian Institute of Technology Bombay, Mumbai 400076 India;1. Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy;2. Structural Mechanics and Concepts Branch, NASA Langley Research Center, Mail Stop 190, Hampton, VA 23681-2199, USA;1. State Key Laboratory of Mechanical System and Vibration, Shanghai Key Lab of Digital Manufacture for Thin-Walled Structures, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China;2. State Key Laboratory of Ocean Engineering and School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China;3. Department of Civil and Environmental Engineering, Washington State University, Pullman, WA 99164-2910, USA |
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| Abstract: | ![]()
The basic equations of the Mindlin theory are specified as starting point for its modification in which total deflection and rotations are split into pure bending deflection and shear deflection with bending angles of rotation, and in-plane shear angles. The equilibrium equations of the former displacement field are split into one partial differential equation for flexural vibrations. In the latter case two differential equations for in-plane shear vibrations are obtained, which are similar to the well-known membrane equations. Rectangular shear locking-free finite element for flexural vibrations is developed. For in-plane shear vibrations ordinary membrane finite elements can be used. Application of the modified Mindlin theory is illustrated in a case of simply supported square plate. Problems are solved analytically and by FEM and the obtained results are compared with the relevant ones available in the literature. |
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| Keywords: | Mindlin plate Flexural and shear vibrations Analytical solution FEM Shear locking |
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