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Article
Frequency convergence characteristics of lumped mass Galerkin meshfree methods
Due to the considerable complexity of meshfree approximants, there still lacks a rational theoretical estimate on the frequency accuracy of lumped mass meshfree methods. In this study, a detailed theoretical a...
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Article
An aspect ratio dependent lumped mass formulation for serendipity finite elements with severe side-length discrepancy
The frequency solutions of finite elements may significantly deteriorate as the mesh aspect ratios become large, which implies a severe element side-length discrepancy. In this work, an aspect ratio dependent ...
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Article
A unified reproducing kernel gradient smoothing Galerkin meshfree approach to strain gradient elasticity
A unified reproducing kernel gradient smoothing formulation is presented for efficient Galerkin meshfree analysis of strain gradient elasticity problems with particular reference to high order basis functions,...
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Article
A least squares recursive gradient meshfree collocation method for superconvergent structural vibration analysis
A least squares recursive gradient meshfree collocation method is proposed for the superconvergent computation of structural vibration frequencies. The proposed approach employs the recursive gradients of mesh...
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Article
Dynamic Analysis of Bubble Attachment and Swee** on Microwire in Subcooled Nucleate Pool Boiling
With the development of industrial technology, heat transfer at the microscale has attracted more and more attention. In this work, 200 μm platinum wire and 150 μm nickel-chromium wire were used as experimenta...
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Article
A Petrov–Galerkin finite element-meshfree formulation for multi-dimensional fractional diffusion equations
Meshfree methods with arbitrary order smooth approximation are very attractive for accurate numerical modeling of fractional differential equations, especially for multi-dimensional problems. However, the non-...
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Article
Arbitrary order recursive formulation of meshfree gradients with application to superconvergent collocation analysis of Kirchhoff plates
A general arbitrary order recursive gradient formulation is presented for meshfree approximation. According to this method, an nth order recursive meshfree gradient is formulated as an interpolation of the (n − 1...
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Article
An efficient gradient smoothing meshfree formulation for the fourth-order phase field modeling of brittle fracture
A reproducing kernel gradient smoothing meshfree formulation is proposed for the fourth-order phase field modeling of brittle fracture. In order to circumvent the complexity and lower efficiency of meshfree gr...
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Article
A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations
Due to the nonlocal property of the fractional derivative, the finite element analysis of fractional diffusion equation often leads to a dense and non-symmetric stiffness matrix, in contrast to the conventiona...
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Article
A unified quadrature-based superconvergent finite element formulation for eigenvalue computation of wave equations
A simple and unified finite element formulation is presented for superconvergent eigenvalue computation of wave equations ranging from 1D to 3D. In this framework, a general method based upon the so called ...
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Article
A superconvergent isogeometric formulation for eigenvalue computation of three dimensional wave equation
A superconvergent isogeometric formulation is presented to compute the eigenvalues for three dimensional wave equation. This three dimensional superconvergent isogeometric formulation is characterized by a hig...
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Article
Upper bound shakedown analysis with the nodal natural element method
In this paper, a novel numerical solution procedure is developed for the upper bound shakedown analysis of elastic-perfectly plastic structures. The nodal natural element method (nodal-NEM) combines the advant...
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Article
Quasi-convex reproducing kernel meshfree method
A quasi-convex reproducing kernel approximation is presented for Galerkin meshfree analysis. In the proposed meshfree scheme, the monomial reproducing conditions are relaxed to maximizing the positivity of the...
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Article
A Hermite reproducing kernel Galerkin meshfree approach for buckling analysis of thin plates
A Hermite reproducing kernel Galerkin meshfree approach is proposed for buckling analysis of thin plates. This approach employs the Hermite reproducing kernel meshfree approximation that incorporates both the ...
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Article
A strain smoothing formulation for NURBS-based isogeometric finite element analysis
A strain smoothing formulation for NURBS (non-uniform rational B-splines) based isogeometric finite element analysis is presented. This approach is formulated within the framework of assumed strain methods and...
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Article
Dispersion and transient analyses of Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration for thin beam and plate structures
A dispersion analysis is carried out to study the dynamic behavior of the Hermite reproducing kernel (HRK) Galerkin meshfree formulation for thin beam and plate problems. The HRK approximation utilizes both th...
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Article
Free vibration analysis of thin plates using Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration
A Hermite reproducing kernel (HRK) Galerkin meshfree formulation is presented for free vibration analysis of thin plates. In the HRK approximation the plate deflection is approximated by the deflection as well...
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Article
A locking-free meshfree curved beam formulation with the stabilized conforming nodal integration
A locking-free meshfree curved beam formulation based on the stabilized conforming nodal integration is presented. Motivated by the pure bending solutions of thin curved beam, a meshfree approximation is const...