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A non-classical Mindlin plate model incorporating microstructure, surface energy and foundation effects
1Department of Mechanical Engineering , Southern Methodist University , PO Box 750337, Dallas, TX 75275-0337, USA.
Proceedings. Mathematical, Physical, and Engineering Sciences
|August 6, 2016
Summary
A new non-classical plate model integrates microstructure, surface energy, and elastic foundation effects for Mindlin plates. This unified approach enhances understanding of advanced plate behaviors in engineering applications.
Area of Science:
- Solid Mechanics
- Materials Science
- Structural Engineering
Background:
- Classical plate theories often neglect microstructural, surface, and foundation effects.
- Mindlin plate theory accounts for transverse shear deformation but can be extended.
- Winkler-Pasternak models offer a two-parameter approach to elastic foundations.
Purpose of the Study:
- To develop a comprehensive non-classical model for Mindlin plates on elastic foundations.
- To unify the treatment of microstructure, surface energy, and foundation effects.
- To provide a general formulation for analyzing advanced plate behaviors.
Main Methods:
- Utilized modified couple stress theory for microstructure.
- Incorporated surface elasticity theory for surface energy effects.
- Employed a two-parameter Winkler-Pasternak foundation model.
- Derived equations of motion and boundary conditions via Hamilton's principle.
Main Results:
- Developed a general non-classical Mindlin plate model with five kinematic variables.
- The model includes material length-scale, surface elastic constants, and foundation parameters.
- The model recovers classical, Kirchhoff, and Timoshenko beam theories as special cases.
- Analytical solutions for static bending and free vibration of a simply supported rectangular plate were obtained.
Conclusions:
- The unified model effectively captures complex plate behaviors.
- The formulation provides a versatile tool for analyzing micro-structured and surface-sensitive plates on foundations.
- Demonstrated the model's applicability through static and dynamic analyses of a rectangular plate.
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