1,721,118 research outputs found
An investigation over the effects of anisotropy on the convergence of the Ritz method for thin and thick composite plates
No full textAnalyse numérique des structures sandwiches viscoélastiques à dérivées fractionnaires / Numerical analysis of viscoelastic sandwich structures by a fractional derivative model
Full text linkMechanical Response of Composite Plates by Means of a Sublaminate Generalized Unied Formulation and Ritz Solution
No full textDynamic Analysis of Multilayered Plates with Viscoelastic Layers Using a Sublaminate Generalized Unified Formulation
No full textAn Analysis Tool for Composite Plates Based on the Ritz Method and a Sublaminate Generalized Unified Formulation
No full textTwo higher order Zig-Zag theories for the accurate analysis of bending, vibration and buckling response of laminated plates by radial basis functions collocation and a unified formulation
No full textIn this article, we combine the Carreras Unified Formulation, CUF (Carrera E. Theories and Finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarking. Arch. Comput. Methods Eng., 2003; 10: 215-297.) and a radial basis function collocation technique for predicting the static deformations, free vibrations and buckling behavior of thin and thick cross-ply laminated plates. We develop by the CUF two Zig-Zag theories according to Murakamis Zig-Zag function. Both theories account for through-the-thickness deformations, allowing the analysis of thick plates. The accuracy and efficiency of this collocation technique for static, vibration, and buckling problems are demonstrated through numerical examples. © 2011 The Author(s)
Extension to Piezoelectric Plates of the Ritz Sublaminate Generalized Unified Formulation Approach
No full textThe Sublaminate Generalized Unified Formulation (SGUF) is a variable kinematics plate modeling approach and is here extended to composite plates including piezoelectric plies. The two-dimensional plate equations are obtained upon defining a priori the through-thickness distribution of the generalized displacements, i.e., the displacement field and the electric potential. According to SGUF, independent approximations can be adopted for the four components of the generalized displacements, which encompass: an Equivalent Single Layer (ESL) or Layer- Wise (LW) description over an arbitrary group of physical plies constituting the composite plate (the sublaminate) and the polynomial order that is employed in each sublaminate. The solution of the two-dimensional piezoelectric plate equations is subsequently sought in weak form by means of a Ritz method. Boundary functions are thus used in conjunction with the domain approximation, whose orthogonal basis may be spanned by trigonometric functions, Chebyshev polynomials or Legendre polynomials. Free-vibration problems as well as static problems involving actuator and sensor configurations are addressed. Three validation case studies are first presented, which demonstrate the high accuracy of the proposed Ritz method in conjunction with high order models. A model assessment is then proposed for showcasing to which extent the flexible SGUF approach allows a reduction of the number of unknowns with a controlled impact on the accuracy of the response
Analysis of Plates and Sandwich Structures Subjected to Non-Classical Boundary Conditions
No full textAnalysis of sandwich plates by Radial Basis Functions collocation, according to Murakami's Zig-Zag theory
No full textIn this article, the static analysis of sandwich plates is performed by radial basis functions collocation, according to the Murakami's Zig-Zag function theory. The Murakami's Zig-Zag function theory accounts for through-the-thickness deformation, by considering a Zig-Zag evolution of the transverse displacement with the thickness coordinate. The equations of motion and the boundary conditions are obtained by the Carrera's unified formulation, and further interpolated by collocation with radial basis functions. © The Author(s) 2012 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav
On the application of the Ritz method to free vibration and buckling analysis of highly anisotropic plates
Full text linkIn this paper insights are provided into the implementation and use of the Ritz method for free vibration and buckling analysis of composite plates. Focus is given on the choice of the trial functions in relation to the degree and the kind of anisotropy exhibited by the plates. The Ritz approximation is applied to models based both on the classical lamination theory and a more advanced variable-kinematic formulation, capable of dealing with several higher order plate theories within an unified framework. A very efficient computation of the Ritz integrals is proposed, which allows to handle hundreds of admissible functions. In this way, accurate upper bound solutions can be obtained even for problems where the convergence rate of the Ritz method is low due to extreme levels of anisotropy. The effect of different forms of elastic couplings, boundary conditions and amount of material anisotropy on the convergence and accuracy of the solution is investigated when different sets of admissible functions – Legendre and Chebyshev polynomials, as well as of trigonometric type – are adopted. Important remarks about the completeness and numerical efficiency of the selected basis are also provided
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