Search results for "X-Ritz method"
showing 3 items of 3 documents
Buckling and post-buckling analysis of cracked stiffened panels via an X-Ritz method
2019
Abstract A multi-domain eXtended Ritz formulation, called X-Ritz, for the analysis of buckling and post-buckling of stiffened panels with cracks is presented. The theoretical framework is based on the First-order Shear Deformation Theory and accounts for von Karman's geometric nonlinearities. The structure is modeled as assembly of plate elements. Penalty techniques are used to fulfill the continuity condition along the edges of contiguous elements and to satisfy essential boundary conditions requirements. The use of an extended set of approximating functions allows to model through-the-thickness cracks and to capture the crack opening and tip singular fields as well as the structural behav…
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.
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…