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A numerical scheme for geometrically exact flexoelectric microbeams using the weak form quadrature element method
In this article, a geometrically exact flexoelectric beam model and its weak form quadrature element formulation are established. The coupling of...
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Nonlinear Bifurcation and Post-buckling Analysis of Cylindrical Composite Stiffened Laminates Based on Weak Form Quadrature Element Method
This paper presents a weak form quadrature element formulation in the analysis of nonlinear bifurcation and post-buckling of cylindrical composite...
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A novel formulation for the weak quadrature element method for solving vibration of strain gradient graded nonlinear nanobeams
A novel formulation of the weak form quadrature element method, referred to as the locally adaptive weak quadrature element method, is proposed to...
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Electromechanical coupling analysis of geometrically exact functionally graded piezoelectric shells based on weak form quadrature element method
In this study, a numerical model for electro-mechanical coupling analysis of geometrically nonlinear functionally graded piezoelectric shell is...
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Nonlinear dynamics of three-dimensional curved geometrically exact beams by a quadrature element formulation
Nonlinear dynamic analyses of three-dimensional (3D) curved geometrically exact beams were carried out using a quadrature element (QEM) formulation....
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An Adapted Formulation for the Locally Adaptive Weak Quadrature Element Method Using Gauss-Lobatto Points
In this manuscript, the Gauss-Lobatto-Legendre (GLL) points is proposed as an alternative to formulate elements of the Locally adaptive Weak...
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Weak-Form Quadrature Element Method: A Comparative Review of Different Formulations and Its Comprehensive Assessment
As a relatively new computational method, the weak-form quadrature element method (QEM) has attracted more and more worldwide attention recently....
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Weak form quadrature elements based on absolute nodal coordinate formulation for planar beamlike structures
Geometrically nonlinear analysis of planar beamlike structures is conducted using weak form quadrature elements that are established on the basis of...
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A lumped mass finite element formulation with consistent nodal quadrature for improved frequency analysis of wave equations
A lumped mass finite element formulation with consistent nodal quadrature is presented for improved frequency analysis of wave equations with...
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An improved formulation for reduced quadrature in computational solid mechanics
In this paper we develop a modification of the recently proposed Taylor series expansion-based formulation for computational solids to satisfy a...
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Weak-form differential quadrature finite elements for functionally graded micro-beams with strain gradient effects
This paper proposes weak-form differential quadrature finite elements for strain gradient functionally graded (FG) Euler–Bernoulli and Timoshenko...
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Weak form quadrature elements for non-classical Kirchhoff plate theory
In this paper, two novel versions of weak form quadrature elements are developed for bending, free vibration and stability analysis of non-classical...
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A Review of Basic Finite Element Procedures
A thorough review of all basic (fundamental) components of the finite element (FE) procedures is presented in this chapter, which includes the “weak...
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A variational differential quadrature solution to finite deformation problems of hyperelastic shell-type structures: a two-point formulation in Cartesian coordinates
A new numerical approach is presented to compute the large deformations of shell-type structures made of the Saint Venant-Kirchhoff and Neo-Hookean...
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A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method
The purpose of this paper is to provide a high-order finite element method (FEM) formulation of nonlocal nonlinear nonlocal graded Timoshenko based...
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Assessment of EqP in XFEM for weak discontinuities
This work analyzes the use of Equivalent Polynomials (EqP) in the context of the eXtended Finite Element Method (XFEM). Special attention is devoted...
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Virtual element formulation for gradient elasticity
The virtual element method has been developed over the last decade and applied to problems in solid mechanics. Different formulations have been used...
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A convected particle Gauss-quadrature interpolation for the cell crossing error reduction
Convected particle domain interpolation (CPDI) is a developed extension technique of the material point method (MPM), which can effectively reduce...
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Stability and Conditioning of Immersed Finite Element Methods: Analysis and Remedies
This review paper discusses the developments in immersed or unfitted finite element methods over the past decade. The main focus is the analysis and...
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A general-purpose meshfree Kirchhoff–Love shell formulation
A thin shell formulation is developed for the approximation by a meshfree Reproducing Kernel Particle Method (RKPM). The formulation is derived from...
