Related papers: An Analysis of Nonlinear Thickness-shear Vibration…
Chladni patterns of vibrating membranes or thin plates faszinated the people already in the eighteenth century. As a simple way to visualize acoustic phenomena it is a valuable experiment for beginners' courses. In this paper I present…
The proposed two-dimensional geometrically exact beam element extends our previous work by including the effects of shear distortion, and also of distributed forces and moments acting along the beam. The general flexibility-based…
A lattice dynamical formalism based on nonaffine response theory is derived for non-centrosymmetric crystals, accounting for long-range interatomic interactions using the Ewald method. The framework takes equilibrated static configurations…
In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully…
A new $n-$ noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element,…
This paper presents the Finite Element Method for Cosserat plates. The mathematical model for Cosserat elastic plates is based on the calculation of the optimal value of the splitting parameter. We discuss the existence and uniqueness of…
One approach for the simulation of metamaterials is to extend an associated continuum theory concerning its kinematic equations, and the relaxed micromorphic continuum represents such a model. It incorporates the Curl of the nonsymmetric…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…
We aimed to use finite element method to simulate the unique behaviors of liquid crystal elastomer, such as semi-soft elasticity, stripe domain instabilities etc. We started from an energy functional with the 2D Bladon-Warner-Terentjev…
This paper presents a novel exact finite element formulation of quasi-3D beam for high-fidelity analysis of functionally graded sandwich beams. Unlike conventional displacement-based elements that rely on approximate interpolation functions…
Calculations of the photonic band structure, transmission coefficients, and quality factors of various two-dimensional, periodic and aperiodic, dielectric photonic crystals by using the finite element method (FEM) are reported. The…
In the present thesis, a computational framework for the analysis of the deformation and damage phenomena occurring at the micro-scale of polycrystalline materials is presented. Micro-mechanics studies are commonly performed using the…
A phase-field description of brittle fracture is employed in the reported four-point bending analyses of monolithic and laminated glass plates. Our aims are: (i) to compare different phase-field fracture formulations applied to thin glass…
Classical methods of sound absorption present fundamental limits that can be overcome by using nonlinear effects. Thin clamped plates have been identified as strongly nonlinear elements, capable of transferring the acoustic power of an…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
This paper presents a combined numerical-theoretical study of the macroscopic behavior and local field distributions in a special class of two-dimensional periodic composites with viscoplastic phases. The emphasis is on strongly nonlinear…
We apply the finite-element lattice equations of motion for quantum electrodynamics to an examination of anomalies in the current operators. By taking explicit lattice divergences of the vector and axial-vector currents we compute the…
We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…