Search results for "Plate theory"
showing 8 items of 18 documents
A family of higher-order single layer plate models meeting Cz0-requirements for arbitrary laminates
2019
Abstract In the framework of displacement-based equivalent single layer (ESL) plate theories for laminates, this paper presents a generic and automatic method to extend a basis higher-order shear deformation theory (polynomial, trigonometric, hyperbolic…) to a multilayer C z 0 higher-order shear deformation theory. The key idea is to enhance the description of the cross-sectional warping: the odd high-order C z 1 function of the basis model is replaced by one odd and one even high-order function and including the characteristic zig-zag behaviour by means of piecewise linear functions. In order to account for arbitrary lamination schemes, four such piecewise continuous functions are consider…
Mixed finite elements for nonlocal elastic multilayered composite plate refined theories
2020
Abstract A novel mixed finite element formulation for the layerwise analysis of nonlocal multilayered composite plates is presented. The finite elements are formulated starting from the weak form of a set of governing equations for the laminate layers that were deduced via the Reissner Mixed Variational Theorem. The primary variables, namely displacements and out-of-plane stresses, are expressed at layer level as through-the-thickness expansions of suitable selected functions with coefficients approximated by the finite element scheme. The through-the-thickness expansion order is considered as a free parameter. This way, finite elements for different refined higher order plate theories can …
Variational formulations and extra boundary conditions within stress gradient elasticity theory with extensions to beam and plate models
2016
Abstract The principle of minimum total potential energy and the primary principle of virtual power for stress gradient elasticity are presented as kinematic type constructs dual of analogous static type principles from the literature (Polizzotto, 2014; Polizzotto, 2015a). The extra gradient-induced boundary conditions are formulated as “boundary congruence conditions” on the microstructure’s deformation relative to the continuum, which ultimately require that the normal derivative of the stresses must vanish at the boundary surface. Two forms of the governing PDEs for the relevant boundary-value problem are presented and their computational aspects are discussed. The Timoshenko beam and th…
A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates
2020
Abstract In this work, a novel high-resolution formulation for multilayered composite plates is presented. The formulations is referred to as high-resolution since it combines (i) Layer-Wise plate theories, which are based on a per-layer, high-order expansion of the primary variables throughout the plate’s thickness, providing a detailed layer-level description of the sought solution; (ii) The discontinuous Galerkin method, a numerical approach based on a discontinuous representation of the unknown fields over the mesh elements and on the introduction of boundary integral operators enforcing inter-element continuity, which allow the natural treatment of high-order mesh elements and provide …
Layer-Wise Discontinuous Galerkin Methods for Piezoelectric Laminates
2020
In this work, a novel high-order formulation for multilayered piezoelectric plates based on the combination of variable-order interior penalty discontinuous Galerkin methods and general layer-wise plate theories is presented, implemented and tested. The key feature of the formulation is the possibility to tune the order of the basis functions in both the in-plane approximation and the through-the-thickness expansion of the primary variables, namely displacements and electric potential. The results obtained from the application to the considered test cases show accuracy and robustness, thus confirming the developed technique as a supplementary computational tool for the analysis and design o…
Estimates for Divergence Velocities of Axially Moving Orthotropic Thin Plates
2014
Some models for axially moving orthotropic thin plates are investigated analytically via methods of complex analysis to derive estimates for critical plate velocities. Linearised Kirchhoff plate theory is used, and the energy forms of steady-state models are considered with homogeneous and inhomogeneous tension profiles in the cross direction of the plate. With the help of the energy forms, some limits for the divergence velocity of the plate are found analytically. In numerical examples, the derived lower limits for the divergence velocity are analysed for plates with small flexural rigidity. peerReviewed
Complete in-plane elastic characterisation under tensile tests of angle-ply laminates composed of polymer-matrix layers
2002
In this paper we present a new strategy to completely characterise the in-plane elastic properties of a large range of angle-ply laminates using only unidirectional tests. We consider laminates having the same number of identical plies in the α and – α directions. This new method uses some preceding results found by Verchery for orthotropic laminates, namely the conditions of existence of a specific direction ω, in which the shear-extension coupling is null. The characterisation of the laminate is then made using the results of three tensile tests: two in the orthotropy axes, and the third one in the ω direction, in order to have always a pure one-dimensional state of stress. We show that …
An implicit mesh discontinuous Galerkin formulation for higher-order plate theories
2019
In this work, a discontinuous Galerkin formulation for higher-order plate theories is presented. The starting point of the formulation is the strong form of the governing equations, which are derived in the context of the Generalized Unified Formulation and the Equivalent Single Layer approach from the Principle of Virtual Displacements. To express the problem within the discontinuous Galerkin framework, an auxiliary flux variable is introduced and the governing equations are rewritten as a system of first-order partial differential equations, which are weakly stated over each mesh element. The link among neighboring mesh elements is then retrieved by introducing suitably defined numerical …