Seamless-domain method: a meshfree multiscale numerical analysis

Mechanical Engineering Journal

2017

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We present a domain decomposition technique combining the finite-element analysis and a multiscale simulation scheme that is termed the seamless-domain method. This technique is applicable to any type of linear problems and has the below different features from conventional substructuring techniques used for finite-element methods such as the super-elements. Adjacent substructures do not need to have the same finite-element mesh or the same node layout at their interface. Therefore, the proposed technique allows us to connect a substructure having a coarse mesh and another substructure having a fine mesh. Additionally, the neighboring substructures are partially overlapped each other around their interfacial region. The overlapped region attempts to generate continuous dependent-variable distribution(s) at the interfacial region. We present four types of numerical experiments related to linear elasticity to investigate practical feasibility of the proposed technique and evaluate an effect of different finite-element meshes in region shared by two substructures on the computational accuracy.

Section: L-shaped Beammentioning

confidence: 99%

Section: Differences Compared With the Standard Super-elementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A domain decomposition technique based on the multiscale seamless-domain method

Mechanical Engineering Journal

2017

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“…Practical application of the proposed SDM technique to a real-size composite having enormous number of inclusions are excluded here because they are illustrated in Appendix. Unless heat enters from outside the system, Equation (1) is a linear heat conduction equation and can be accurately solved using the previous version of the SDM (linear solver) presented in Subsection 2.3 and (Suzuki and Soga, 2016).…”

Section: Procedures Of the Sdm 21 Problem Statementmentioning

confidence: 99%

“…In previous work (Suzuki and Soga, 2016, Suzuki, 2016a, 2016b, a multiscale analysis called the seamless-domain method (SDM) was developed and applied to linear analyses. When conducting a macroscopic analysis of an entire field, the SDM constructs a meshfree model that is represented by only a small number of coarse-grained points (CPs).…”

Section: Introductionmentioning

confidence: 99%

Multiscale seamless-domain method for solving nonlinear heat conduction problems without iterative multiscale calculations

Mechanical Engineering Journal

Todoroki

Mizutani

2016

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In this paper, we applied a multiscale numerical scheme called the seamless-domain method (SDM) to nonlinear elliptic boundary value problems. Although the SDM is meshfree, it can obtain a high-resolution solution whose dependent-variable gradient(s) is sufficiently smooth and continuous. The SDM models with only coarse-grained points can produce accurate solutions for both linear heat conduction problems and linear elastic problems. This manuscript presents a simple nonlinear solver for the SDM analysis of heterogeneous materials. Although the solver can easily approximate the solutions to nonlinear multiscale problems, it does not require an iterative multiscale analysis at every convergence calculation. In other words, the proposed scheme does not completely interactively couple the multiple scales. We present numerical examples of nonlinear stationary heat conduction analyses of heterogeneous fields and compare the SDM model, the direct finite-element model, and the homogenized model based on the homogenization theory. For a real heterogeneous structure (graphite fiber composite) that did not have strong material nonlinearities, the SDM model using only 925 points gave a solution with similar precisions as an ordinary finite element solution using hundreds of thousands of nodes. To investigate the limitations of the method, we also applied the SDM to imaginary materials with various strengths of thermal property nonlinearities.

Multiscale seamless‐domain method for linear elastic analysis of heterogeneous materials

Numerical Meth Engineering

2015

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SUMMARYA multiscale numerical technique, termed the seamless-domain method (SDM), is applied to linear elastic problems. The SDM consists of two steps. The first step is a microscopic analysis of the local simulated domain to construct interpolation functions for discretizing governing equations. This allows an SDM solution to represent a structure consisting of heterogeneous microstructure(s) without homogenization. The second step is a macroscopic analysis of a seamless global (entire) domain that has only coarse-grained points and does not need a mesh or grid. The special functions obtained in the first step are used in interpolating the dependent-variable distribution in the global domain. Additionally, the SDM can enhance analytical precision and resolution when analyzing both homogeneous and heterogeneous fields. Our previous manuscript gave numerical examples of the application of the method to scalar temperature fields. To investigate the feasibility of the analysis of vector fields, the SDM technique is applied in linear elastic analysis of heterogeneous materials in the present study. The SDM's global models with only a few hundred points gave shear locking-free and hourglass-free solutions at the same level of accuracy as solutions obtained from conventional finite element analysis using hundreds of thousands of node points or more.