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A Ritz formulation for non-linear analysis of damage initiation and evolution in variable angle tow composite plates under progressive loading is presented. The model is built on a few key items. It assumes first order shear deformation theory kinematics and non-liner strains in the von Kármán sense. The constitutive relationships are formulated in the framework of continuum damage mechanics at the ply level, so that each laminate layer can experience in-plane damage initiation and evolution, then reflected in material softening and loss of local stiffness. A Ritz polynomial expansion of the primary variables and the minimization of the total potential energy provide the discrete solution equations, which are then solved with an incremental-iterative approach for capturing damage evolution. A few tests have been successfully performed to validate the approach. Eventually, some original results about variable angle tow plates under progressive in-plane compression loads highlight the effect of damage on the post-buckling response. [ABSTRACT FROM AUTHOR]

In the present work, nonlocal layer-wise (LW) models for the analysis of magneto-electro-elastic multilayered plates are formulated. An Eringen non-local continuum behavior is assumed for the layers material; in particular, as usual in plate theories, partial in-plane nonlocality is assumed whereas local constitutive behavior is considered in the thickness direction. The proposed plate theories are obtained via the Reissner mixed variational theorem (RMVT), assuming the generalized displacements and generalized out-of-plane stresses as primary variables, and expressing them as through-the-thickness expansions of suitably selected functions, considering the expansion order as a free parameter. In the framework of the Carrera Unified Formulation, this allows the systematic generation of advanced high order plate theories via a layer-based assembly algorithm of the so-called fundamental nuclei associated with the variables expansion terms. The use of the LW approach and RMVT allows for (i) the explicit fulfillment of the transverse generalized stress interface equilibrium, which is crucial for a correct description of the plate fields, (ii) the straightforward analysis of plates with layers exhibiting different characteristic lengths in their nonlocal behavior. A Navier solution for the developed models has been implemented and tested for the static bending and free vibrations analyses of rectangular simply-supported plates. The obtained representative results favorably compare against available three-dimensional analytic results and demonstrate the features of the proposed theories. [ABSTRACT FROM AUTHOR]

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 fluxes, whose explicit expressions define the proposed Interior Penalty discontinuous Galerkin formulation. Furthermore, to account for the presence of generally curved boundaries of the considered plate domain, the discretisation mesh is built by combining a background grid and an implicit representation of the domain. hp-convergence analyses and a comparison with the results obtained using the Finite Element Method are provided to show the accuracy of the proposed formulation as well as the computational savings in terms of overall degrees of freedom. [ABSTRACT FROM AUTHOR]