Riccardo Vescovini | Searcharxiv

arXiv2026

A Comprehensive p-VEM Framework for Advanced Variable Stiffness Plates with Arbitrary Shapes

This paper presents a comprehensive, high-order (p-version) Virtual Element Method (VEM) framework for the structural analysis of innovative variable stiffness plates. VEM is particularly suited for complex configurations due to its ability to handle arbitrary polygonal meshes, including curved edges. However, its mathematical formulation may hinder its spread in the engineering community. This work illustrates a formulation with an accessible implementation using well-known FEM notation and integrating at the same time a set of new advanced capabilities. Specifically, both standard stabilized and advanced self-stabilized strategies are adopted. To further improve the robustness of VEM in the presence of variable coefficients, polynomial projections taking into account the coefficients are employed. This approach is referred to as Variable Coefficients-VEM approach (VC-VEM). This unified framework is applied to linear static, free-vibration, and buckling analyses, and validated against analytical solutions and numerical benchmarks. In particular, plates with cutouts and problems featuring high-gradient solutions are investigated, demonstrating that the proposed comprehensive approach provides a flexible and ready-to-implement tool for advanced structural design.

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arXiv2026

Benchmarking stabilized and self-stabilized p-virtual element methods with variable coefficients

Standard Virtual Element Methods (VEM) are based on polynomial projections and require a stabilization term to evaluate the contribution of the non-polynomial component of the discrete space. However, the stabilization term is not uniquely defined by the underlying variational formulation and is typically introduced in an ad hoc manner, potentially affecting the numerical response. Stabilization-free and self-stabilized formulations have been proposed to overcome this issue, although their theoretical analysis is still less mature. This paper provides an in-depth numerical investigation into different stabilized and self-stabilized formulations for the p-version of VEM. The results show that self-stabilized and stabilization-free formulations achieve optimal accuracy while suffering from worse conditioning. Moreover, a new projection operator, which explicitly accounts for variable coefficients, is introduced within the framework of standard virtual element spaces. Numerical results show that this new approach is more robust than the existing ones for large values of p.

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