Search results for " Ritz method"
showing 10 items of 11 documents
A non-linear Ritz method for progressive failure analysis of variable angle tow composite laminates
2022
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 Karman 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 e…
X-Ritz Solution for Nonlinear Free Vibrations of Plates with Embedded Cracks
2019
The analysis of large amplitude vibrations of cracked plates is considered in this study. The problem is addressed via a Ritz approach based on the first-order shear deformation theory and von Karman’s geometric nonlinearity assumptions. The trial functions are built as series of regular orthogonal polynomial products supplemented with special functions able to represent the crack behaviour (which motivates why the method is dubbed as eXtended Ritz); boundary functions are used to guarantee the fulfillment of the kinematic boundary conditions along the plate edges. Convergence and accuracy are assessed to validate the approach and show its efficiency and potential. Original results are then…
Post-buckling analysis of cracked multilayered composite plates by pb-2 Rayleigh–Ritz method
2015
Abstract A pb-2 Rayleigh–Ritz variational approach for the analysis of post-buckling behavior of cracked composite plates is presented. The plate is modeled by the first order shear deformation theory taking geometric nonlinearities into account through the von Karman’s theory. General stacking sequences are considered. Cracks are modeled by using subdomain decomposition of the plate coupled with penalty techniques, used to augment the variational statement with the needed continuity conditions along the connected subdomains edges. Numerical procedures have been developed and used to validate the present solution by comparison with available literature results. Original results are then pre…
Post-Buckling Analysis of Damaged Multilayered Composite Stiffened Plates by Rayleigh-Ritz Method
2016
A Rayleigh-Ritz approach for the analysis of buckling and post-buckling behavior of cracked composite stiffened plates is presented. The structure is modeled as the assembly of plate elements modeled by the first order shear deformation theory and taking geometric nonlinearities into account through the von Karman’s theory assumptions. Continuity along the plate elements connected edges and the enforcement of rigid and elastic restraints of the plate boundaries are obtained by using penalty techniques, which also allow to straightforwardly implement efficient crack modeling strategies. General symmetric and unsymmetric stacking sequences are considered and numerical procedures have been dev…
A single-domain Ritz approach for buckling and post-buckling analysis of cracked plates
2019
Abstract A Ritz approach for the analysis of buckling and post-buckling of plates with through-the-thickness cracks is presented. The plate behavior is described by the first order shear deformation theory and von Karman’s geometric nonlinearity. The admissible functions used in the displacements approximation are series of regular orthogonal polynomial supplemented with special functions able to decribe the dicontinuity across the crack and the singularity at the crack tips; boundary functions are used to fullfill the homogeneous essential boundary conditions. Convergence studies and analysis results are presented for buckling and post-buckling of plates with a central through-the-thicknes…
Buckling and post-buckling of variable stiffness plates with cutouts by a single-domain Ritz method
2023
Structural components with variable stiffness can provide better performances with respect to classical ones and offer an enlarged design space for their optimization. They are attractive candidates for advanced lightweight structural applications whose functionalities often impose the presence of cutouts that requires accurate and effective analysis for their design. In the present work, a single-domain Ritz formulation is proposed, implemented and validated for the analysis of buckling and post-buckling behaviour of variable stiffness plates with cutouts. The plate model is based on the first-order shear deformation theory with nonlinear von Karman strain–displacement relationships. The p…
A non-linear Ritz method for the analysis of low velocity impact induced dynamics in variable angle tow composite laminates
2021
Abstract Variable angle tow (VAT) laminates feature composite layers reinforced by fibres following continuous curved paths and offer a wide structural design space for the manufacturing of composite components. In this work, a formulation for the analysis of the impact-induced dynamics in VAT laminated plates is proposed, implemented and tested in this work. The method is based on the adoption of first order shear deformation kinematics and includes von Karman non-linear strains. The discrete system is obtained by employing a pb-2 Ritz series expansion into the Hamilton’s variational statement, while the impact loading is modelled through Hertzian contact law. The resulting non-linear gove…
Investigation of buckling characteristics of cracked variable stiffness composite plates by an eXtended Ritz approach
2021
Abstract Variable Angle Tow (VAT) composite plates are characterized by in-plane variable stiffness properties, which opens to new concepts of stiffness tailoring and optimization to achieve higher structural performance for advanced lightweight structures where damage tolerance consideration are often mandatory. In this paper, a single-domain eXtended Ritz formulation is proposed to study the buckling behaviour of variable stiffness laminated cracked plates. The plate behaviour is described by the first order shear deformation theory whose generalized displacements, namely reference plane translations and rotations, are expressed via suitable admissible trial functions. These consist of a …
Postbuckling analysis of cracked stiffned plates by pb–2 Rayleigh-Ritz method
2015
A Rayleigh-Ritz approach for the analysis of buckling and post-buckling behavior of cracked composite stiffened plates is presented. The structure is thought as the assembly of plate elements modeled by the first order shear deformation theory. Continuity along the edges common to contiguous elements are enforced by using penalty techniques, which also allow to straightforwardly implement efficient crack modeling strategies. General symmetric and unsymmetric stacking sequences are considered and numerical procedures have been developed and used to validate the present solution by comparison with FEA results. Original results are also presented for post-buckling solution of multilayered stif…
Free vibrations analysis of cracked variable stiffness composite plates by the eXtended Ritz method
2022
Variable stiffness composite laminates show advantageous structural features related to their enlarged design space. They are attractive candidates for advanced engineering applications where the assessment of static and dynamic behavior and strength in the presence of cracks is often required. In the present work, a single-domain extended Ritz formulation is proposed to study the free vibrations of cracked variable stiffness composite plates. The plate model is based on the first-order shear deformation theory whose primary variable, i.e. displacements and rotations, are approximated via a set of orthogonal polynomial trial functions enriched with a set of special crack functions. These fu…