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Article
Open AccessInterpolation-based immersogeometric analysis methods for multi-material and multi-physics problems
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction ...
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Article
Open AccessA multi-resolution physics-informed recurrent neural network: formulation and application to musculoskeletal systems
This work presents a multi-resolution physics-informed recurrent neural network (MR PI-RNN), for simultaneous prediction of musculoskeletal (MSK) motion and parameter identification of the MSK systems. The MSK...
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Article
Open AccessSupport vector machine guided reproducing kernel particle method for image-based modeling of microstructures
This work presents an approach for automating the discretization and approximation procedures in constructing digital representations of composites from micro-CT images featuring intricate microstructures. The...
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Article
Open AccessAutomated shape and thickness optimization for non-matching isogeometric shells using free-form deformation
Isogeometric analysis (IGA) has emerged as a promising approach in the field of structural optimization, benefiting from the seamless integration between the computer-aided design (CAD) geometry and the analys...
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Article
Open AccessBenchmarking Computational Shell Models
The practice of verification of shell finite element formulations is discussed from a variety of viewpoints: The provenance of benchmark target values, the suitability of benchmark problems for different class...
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Article
Open AccessA deformation-dependent coupled Lagrangian/semi-Lagrangian meshfree hydromechanical formulation for landslide modeling
The numerical modelling of natural disasters such as landslides presents several challenges for conventional mesh-based methods such as the finite element method (FEM) due to the presence of numerically challe...
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Article
Open AccessA semi-Lagrangian reproducing kernel particle method with particle-based shock algorithm for explosive welding simulation
The explosive welding process is an extreme-deformation problem that involves shock waves, large plastic deformation, and fragmentation around the collision point, which are extremely challenging features to m...
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Article
Open AccessA variational multiscale immersed meshfree method for heterogeneous materials
We introduce an immersed meshfree formulation for modeling heterogeneous materials with flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial compatibility condition i...
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Article
Open AccessLevel set topology optimization for design-dependent pressure loads using the reproducing kernel particle method
This paper presents a level set topology optimization method in combination with the reproducing kernel particle method (RKPM) for the design of structures subjected to design-dependent pressure loads. RKPM al...
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Article
RKPM2D: an open-source implementation of nodally integrated reproducing kernel particle method for solving partial differential equations
We present an open-source software RKPM2D for solving PDEs under the reproducing kernel particle method (RKPM)-based meshfree computational framework. Compared to conventional mesh-based methods, RKPM provides...
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Article
Treatment of near-incompressibility in meshfree and immersed-particle methods
We propose new projection methods for treating near-incompressibility in small and large deformation elasticity and plasticity within the framework of particle and meshfree methods. Using the $$\overline{\mathbf ...
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Article
A MUSCL-SCNI approach for meshfree modeling of shock waves in fluids
A stable and nodally integrated meshfree formulation for modeling shock waves in fluids is developed. The reproducing kernel approximation is employed to discretize the conservation equations for compressible ...
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Article
A decomposed subspace reduction for fracture mechanics based on the meshfree integrated singular basis function method
In this work, we propose a new decomposed subspace reduction (DSR) method for reduced-order modeling of fracture mechanics based on the integrated singular basis function method (ISBFM) with reproducing kernel...
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Article
Correction to: A damage analysis for brittle materials using stochastic micro-structural information
After publication of the original article [1], it has come to our attention that a citation of article [2] was missed.
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Article
Analysis of hot cracking during lap joint laser welding processes using the melting state-based thermomechanical modeling approach
Although lap joint laser welding is in great demand in practice, very limited numerical studies have been performed to investigate the hot cracking behavior in this welding configuration. This is because the t...
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Article
Numerical investigation of statistical variation of concrete damage properties between scales
Concrete is typically treated as a homogeneous material at the continuum scale. However, the randomness in micro-structures has profound influence on its mechanical behavior. In this work, the relationship of ...
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Article
Variationally consistent coupling of non-matching discretizations for large deformation problems
Non-matching interfaces occur in large computational models of complicated structures when different discretizations are used in different regions of the problem domain. Presence of non-matching interfaces, fo...
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Article
Stable and flux-conserved meshfree formulation to model shocks
Accurate shock modeling requires that two critical issues be addressed: (1) correct representation of the essential shock physics, and (2) control of Gibbs phenomenon oscillation at the discontinuity. In this ...
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Article
A damage analysis for brittle materials using stochastic micro-structural information
In this work, a micro-crack informed stochastic damage analysis is performed to consider the failures of material with stochastic microstructure. The derivation of the damage evolution law is based on the Helm...
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Reference Work Entry In depth
Meshless and Meshfree Methods