Search results for "Ritz method"
showing 8 items of 18 documents
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…
Nonlinear free vibrations of composite structures via the X-Ritz method
2020
The analysis of large amplitude vibrations of thin-walled cracked structures build as plate assembly is considered in this study. The problem is addressed via a Ritz approach, called X-Ritz, based on the first order shear deformation theory and von K´arm´an’s geometric nonlinearity assumptions. The trial functions are expressed as series of regular orthogonal polynomial products supplemented with special functions able to represent the crack behaviour; boundary functions are used to guarantee the fulfillment of the kinematic boundary conditions. Results are presented, which illustrate the influence of cracks on the stiffening effect due to large amplitude vibrations.
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…
Ritz Solution for Transient Analysis of Variable-Stiffness Shell Structures
2020
The dynamic response of thin-walled structures is driven by mass and stiffness distribution. As such, variable-stiffness (VS) composites offer opportunities to tune structural dynamic responses. To this extent, efficient analysis tools become increasingly important for structural analysis and design purposes. In this work, an efficient and versatile Ritz method for free vibrations and linear transient analysis of VS doubly curved shell structures is presented. VS shell structures are modeled as an assembly of shell-like domains. The shell kinematics is based on the first-order shear deformation theory, and no further assumption is made on the shallowness or on the thinness of the structure.…
Progressive non-linear damage of variable angle tow composite plates by a Ritz approach
2022
In this work a Ritz model for progressive non-linear damage analysis of variable angle tow composite plates is presented. The damage is treated in the framework of continuum damage mechanics and its evolution is based on a linear softening law with which four damage indices are computed for degrading the mechanical properties of the material. A set of analyses have been carried out to investigate how damage evolves in VAT composite plates under progressive loading.