{"title":"Dynamic analysis of rectangular cut-out plates resting on elastic foundation","authors":"Sabyasachi Ghosh, Subham Pal, Salil Haldar","doi":"10.1007/s10999-023-09662-9","DOIUrl":null,"url":null,"abstract":"<div><p>A finite element method using a 9-node isoparametric plate bending element, incorporating the effects of transverse shear based on the first-order shear deformation theory, is proposed for the free vibration analysis of rectangular cut-out plates resting on an elastic foundation. The elastic foundation is modeled on the Winkler and the Pasternak type, and equations of motion are obtained using the principle of virtual work. To account for the parabolic strain variation through the thickness, a shear correction factor of 5/6 is used, and the effect of rotary inertia has been included in the formulation. The present formulation is compared with established results obtained using analytical methods, with and without rotary inertia, and the max variation observed is 2.24% without rotary inertia and 0.02% with rotary inertia. Cut-out plates are validated with results obtained using the finite element method, and the max variation observed between established results and present formulation is 1.3%. Establishing the accuracy of the current formulation, new results are obtained for rectangular cut-out plates resting on an elastic foundation of various stiffness parameters. The effect of incrementing cut-out dimensions and different layouts of cut-outs in the plate on the free vibration response of plates resting on an elastic foundation is investigated, along with the effects of varying aspect ratios and thickness-to-side ratios.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"20 1","pages":"81 - 105"},"PeriodicalIF":2.7000,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mechanics and Materials in Design","FirstCategoryId":"88","ListUrlMain":"https://link.springer.com/article/10.1007/s10999-023-09662-9","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
A finite element method using a 9-node isoparametric plate bending element, incorporating the effects of transverse shear based on the first-order shear deformation theory, is proposed for the free vibration analysis of rectangular cut-out plates resting on an elastic foundation. The elastic foundation is modeled on the Winkler and the Pasternak type, and equations of motion are obtained using the principle of virtual work. To account for the parabolic strain variation through the thickness, a shear correction factor of 5/6 is used, and the effect of rotary inertia has been included in the formulation. The present formulation is compared with established results obtained using analytical methods, with and without rotary inertia, and the max variation observed is 2.24% without rotary inertia and 0.02% with rotary inertia. Cut-out plates are validated with results obtained using the finite element method, and the max variation observed between established results and present formulation is 1.3%. Establishing the accuracy of the current formulation, new results are obtained for rectangular cut-out plates resting on an elastic foundation of various stiffness parameters. The effect of incrementing cut-out dimensions and different layouts of cut-outs in the plate on the free vibration response of plates resting on an elastic foundation is investigated, along with the effects of varying aspect ratios and thickness-to-side ratios.
期刊介绍：
It is the objective of this journal to provide an effective medium for the dissemination of recent advances and original works in mechanics and materials'' engineering and their impact on the design process in an integrated, highly focused and coherent format. The goal is to enable mechanical, aeronautical, civil, automotive, biomedical, chemical and nuclear engineers, researchers and scientists to keep abreast of recent developments and exchange ideas on a number of topics relating to the use of mechanics and materials in design.
Analytical synopsis of contents:
The following non-exhaustive list is considered to be within the scope of the International Journal of Mechanics and Materials in Design:
Intelligent Design:
Nano-engineering and Nano-science in Design;
Smart Materials and Adaptive Structures in Design;
Mechanism(s) Design;
Design against Failure;
Design for Manufacturing;
Design of Ultralight Structures;
Design for a Clean Environment;
Impact and Crashworthiness;
Microelectronic Packaging Systems.
Advanced Materials in Design:
Newly Engineered Materials;
Smart Materials and Adaptive Structures;
Micromechanical Modelling of Composites;
Damage Characterisation of Advanced/Traditional Materials;
Alternative Use of Traditional Materials in Design;
Functionally Graded Materials;
Failure Analysis: Fatigue and Fracture;
Multiscale Modelling Concepts and Methodology;
Interfaces, interfacial properties and characterisation.
Design Analysis and Optimisation:
Shape and Topology Optimisation;
Structural Optimisation;
Optimisation Algorithms in Design;
Nonlinear Mechanics in Design;
Novel Numerical Tools in Design;
Geometric Modelling and CAD Tools in Design;
FEM, BEM and Hybrid Methods;
Integrated Computer Aided Design;
Computational Failure Analysis;
Coupled Thermo-Electro-Mechanical Designs.
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