Free vibration analysis of orthotropic plates resting on Pasternak foundation by mixed finite element formulation

Omurtag, Mehmet H.; Kadıoğlu, Fethi

doi:10.1016/s0045-7949(97)00128-4

Cited by 61 publications

(26 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Thus the total energy of the plate-soil system can be written as; (8) Assuming that, in the plate of Fig. 1, u and v are proportional to z and w is the independent of z [11], one can write the plate displacement at an arbitrary x, y, z in terms of the two slopes and a displacement as follows:…”

Section: Evaluation Of the Stiffness Matrixmentioning

confidence: 99%

Earthquake analysis of thick plates resting on elastic foundation with second order finite element

Özdemir¹

2018

JSEAM

View full text Add to dashboard Cite

The purpose of this paper is to study parametric earthquake analysis of thick plates resting on Winkler foundation using Mindlin's theory, to determine the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick plates subjected to earthquake excitations. In the analysis, finite element method is used for spatial integration and the Newmark-β method is used for the time integration. Finite element formulation of the equations of the thick plate theory is derived by second order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates simply supported and clamped along all four edges. In the analysis, 8-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 8-noded finite element can be effectively used in the earthquake analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

show abstract

Section: Evaluation Of the Stiffness Matrixmentioning

confidence: 99%

Earthquake analysis of thick plates resting on elastic foundation with second order finite element

Özdemir¹

2018

JSEAM

View full text Add to dashboard Cite

show abstract

“…The Gâteaux differential method is a more powerful, reliable and efficient variational tool compared to the widely accepted Hellinger-Reissner (HR) and Hu-Washizu (HW) variational principles, and it has many advantages over these principles. The mentioned techniques are extensively compared in [21] and [22]. The Gâteaux differential method was first used in [23].…”

Section: Introductionmentioning

confidence: 99%

“…For the HR and HW principles, the boundary conditions can be included in the functional by the Lagrange multipliers, whereas in the Gâteaux differential method boundary conditions are completely included by mathematical manipulations. For a detailed discussion about various variational principles, the reader is referred to papers [22,31].…”

Section: Introductionmentioning

confidence: 99%

Alternativno rješenje za križno uslojene kompozitne debele ploče

2016

JCE

View full text Add to dashboard Cite

Alternative solution for cross-ply laminated composite thick platesThe structural analysis of orthotropic and linear elastic cross-ply laminated composite thick plates is made by considering complete effects of transverse shear and normal stresses. The solutions are obtained using the functional analysis method in conjunction with the Gâteaux differential. A new functional with boundary condition terms is developed for the analysis. A four-node serendipity element with eight degrees of freedom is used. To ensure the accuracy of the developed mixed finite element (MFE), numerical results are compared with those of the published solutions. It has been proven that the developed MFE is highly accurate and efficient. Alternativno rješenje za križno uslojene kompozitne debele ploče U radu se opisuje analiza ortotropnih linearnoelastičnih križno uslojenih kompozitnih debelih ploča, pri čemu se u obzir uzima zajedničko djelovanje poprečnih posmičnih i normalnih naprezanja. Rješenja se dobivaju primjenom metoda funkcionalne analize u kombinaciji s Gâteauxovom derivacijom. Za potrebe analize razvijen je novi funkcional sa članovima za rubne uvjete. Primijenjen je serendipity element sa četiri čvora i osam stupnjeva slobode. Kako bi se potvrdila točnost novorazvijenoga mješovitog konačnog elementa , numerički su rezultati uspoređeni s objavljenim rješenjima. Utvrđeno je da je novorazvijeni element izuzetno točan i djelotvoran.

show abstract

“…One of these models is the Pasternak type foundation model. The two parameter model of Pasternak takes into account the effect of shear interaction among the points in the foundation [7][8][9][10]. If the second parameter vanishes, the Pasternak foundation is reduced to the Winkler type.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of non-symmetric FGM sandwich square plate resting on elastic foundations

AddaBedia

Fekrar

Salman

et al. 2014

MATEC Web of Conferences

View full text Add to dashboard Cite

Abstract. In this study, free vibration analysis of simply supported sandwich plate resting on elastic foundation is examined. In this model, the displacements vary as a sinusoidal function across the plate thickness and satisfy zero shear stress condition at the top and bottom surfaces of the plate. The governing equations are derived by employing the principle of Hamilton, These equations are solved via Navier type and the dynamic results are presented by solving eigenvalue problems. The numerical results obtained through the present analysis for free vibration are presented and compared with those available in the literature.

show abstract

Free vibration analysis of orthotropic plates resting on Pasternak foundation by mixed finite element formulation

Cited by 61 publications

References 21 publications

Earthquake analysis of thick plates resting on elastic foundation with second order finite element

Earthquake analysis of thick plates resting on elastic foundation with second order finite element

Alternativno rješenje za križno uslojene kompozitne debele ploče

Free vibration analysis of non-symmetric FGM sandwich square plate resting on elastic foundations

Contact Info

Product

Resources

About