Static Response of 2D FG Porous Plates Resting on Elastic Foundation Using Midplane and Neutral Surfaces with Movable Constraints
The current manuscript develops a novel mathematical formulation to portray the static deflection of a bi-directional functionally graded (BDFG) porous plate resting on an elastic foundation. The correctness of the static response produced by middle surface (MS) vs. neutral surface (NS) formulations...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/24/4784 |
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| author | Ammar Melaibari Salwa A. Mohamed Amr E. Assie Rabab A. Shanab Mohamed A. Eltaher |
| author_facet | Ammar Melaibari Salwa A. Mohamed Amr E. Assie Rabab A. Shanab Mohamed A. Eltaher |
| author_sort | Ammar Melaibari |
| collection | DOAJ |
| description | The current manuscript develops a novel mathematical formulation to portray the static deflection of a bi-directional functionally graded (BDFG) porous plate resting on an elastic foundation. The correctness of the static response produced by middle surface (MS) vs. neutral surface (NS) formulations, and the position of the boundary conditions, are derived in detail. The relation between in-plane displacement field variables on NS and on MS are derived. Bi-directional gradation through the thickness and axial direction are described by the power function; however, the porosity is depicted by cosine function. The displacement field of a plate is controlled by four variables higher order shear deformation theory to satisfy the zero shear at upper and lower surfaces. Elastic foundation is described by the Winkler–Pasternak model. The equilibrium equations are derived by Hamilton’s principles and then solved numerically by being discretized by the differential quadrature method (DQM). The proposed model is confirmed with former published analyses. The numerical parametric studies discuss the effects of porosity type, porosity coefficient, elastic foundations variables, axial and transverse gradation indices, formulation with respect to MS and NS, and position of boundary conditions (BCs) on the static deflection and stresses. |
| first_indexed | 2024-03-09T16:07:54Z |
| format | Article |
| id | doaj.art-30a171883e78483a812e24276fd583a4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:07:54Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-30a171883e78483a812e24276fd583a42023-11-24T16:29:40ZengMDPI AGMathematics2227-73902022-12-011024478410.3390/math10244784Static Response of 2D FG Porous Plates Resting on Elastic Foundation Using Midplane and Neutral Surfaces with Movable ConstraintsAmmar Melaibari0Salwa A. Mohamed1Amr E. Assie2Rabab A. Shanab3Mohamed A. Eltaher4Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah P.O. Box 80204, Saudi ArabiaEngineering Mathematics Department, Faculty of Engineering, Zagazig University, Zagazig P.O. Box 44519, EgyptMechanical Engineering Department, Faculty of Engineering, Jazan University, Jazan P.O. Box 45142, Saudi ArabiaEngineering Mathematics Department, Faculty of Engineering, Zagazig University, Zagazig P.O. Box 44519, EgyptMechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah P.O. Box 80204, Saudi ArabiaThe current manuscript develops a novel mathematical formulation to portray the static deflection of a bi-directional functionally graded (BDFG) porous plate resting on an elastic foundation. The correctness of the static response produced by middle surface (MS) vs. neutral surface (NS) formulations, and the position of the boundary conditions, are derived in detail. The relation between in-plane displacement field variables on NS and on MS are derived. Bi-directional gradation through the thickness and axial direction are described by the power function; however, the porosity is depicted by cosine function. The displacement field of a plate is controlled by four variables higher order shear deformation theory to satisfy the zero shear at upper and lower surfaces. Elastic foundation is described by the Winkler–Pasternak model. The equilibrium equations are derived by Hamilton’s principles and then solved numerically by being discretized by the differential quadrature method (DQM). The proposed model is confirmed with former published analyses. The numerical parametric studies discuss the effects of porosity type, porosity coefficient, elastic foundations variables, axial and transverse gradation indices, formulation with respect to MS and NS, and position of boundary conditions (BCs) on the static deflection and stresses.https://www.mdpi.com/2227-7390/10/24/4784static deflection of BDFG porous platesmiddle and neutral surfacesa four variables high shear deformation theorymovable and immovable BCsnumerical solution |
| spellingShingle | Ammar Melaibari Salwa A. Mohamed Amr E. Assie Rabab A. Shanab Mohamed A. Eltaher Static Response of 2D FG Porous Plates Resting on Elastic Foundation Using Midplane and Neutral Surfaces with Movable Constraints Mathematics static deflection of BDFG porous plates middle and neutral surfaces a four variables high shear deformation theory movable and immovable BCs numerical solution |
| title | Static Response of 2D FG Porous Plates Resting on Elastic Foundation Using Midplane and Neutral Surfaces with Movable Constraints |
| title_full | Static Response of 2D FG Porous Plates Resting on Elastic Foundation Using Midplane and Neutral Surfaces with Movable Constraints |
| title_fullStr | Static Response of 2D FG Porous Plates Resting on Elastic Foundation Using Midplane and Neutral Surfaces with Movable Constraints |
| title_full_unstemmed | Static Response of 2D FG Porous Plates Resting on Elastic Foundation Using Midplane and Neutral Surfaces with Movable Constraints |
| title_short | Static Response of 2D FG Porous Plates Resting on Elastic Foundation Using Midplane and Neutral Surfaces with Movable Constraints |
| title_sort | static response of 2d fg porous plates resting on elastic foundation using midplane and neutral surfaces with movable constraints |
| topic | static deflection of BDFG porous plates middle and neutral surfaces a four variables high shear deformation theory movable and immovable BCs numerical solution |
| url | https://www.mdpi.com/2227-7390/10/24/4784 |
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