Abstract
In this study, it is aimed to analyze the quasi-static response of viscoelastic Kirchhoff plates with mixed finite element formulation based on the Gâteaux differential. Although the static response of elastic plate, beam and shell structures is a widely studied topic, there are few studies that exist in the literature pertaining to the analysis of the viscoelastic structural elements especially with complex geometries, loading conditions and constitutive relations. The developed mixed finite element model in transformed Laplace-Carson space has four unknowns as displacement, bending and twisting moments in addition to the dynamic and geometric boundary condition terms. Four-parameter solid model is employed for modelling the viscoelastic behaviour. For transformation of the solutions obtained in the Laplace-Carson domain to the time domain, different numerical inverse transform techniques are employed. The developed solution technique is applied to several quasi-static example problems for the verification of the suggested numerical procedure.
Highlights
Determination of the behaviour of plate elements is an important engineering problem due to their wide application in all fields of engineering
The aim of the present work is to demonstrate the application of an efficient method, as mentioned above, to the viscoelastic Kirchhoff plates with the model of fourparameter solid type
The numerical solutions of the finite element formulation derived in Laplace-Carson space are transformed to the real time domain using the inverse numerical Laplace transformation
Summary
Determination of the behaviour of plate elements is an important engineering problem due to their wide application in all fields of engineering. The application of the numerical methods to viscoelastic problems has been presented by a number of authors [3,4]. Quasi-static response of viscoelastic plates under time dependent loads are investigated in the Laplace-Carson domain based on the Gâteaux differential method. Based on the Gâteaux differential method, Aköz and his co-workers [913] analysed the quasi- static and dynamic behaviour of the viscoelastic beam and plate elements by employing the Kelvin and/or Three-parameter Kelvin model. The aim of the present work is to demonstrate the application of an efficient method, as mentioned above, to the viscoelastic Kirchhoff plates with the model of fourparameter solid type. Numerical results for quasi-static analysis of viscoelastic plates are presented
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