scholarly journals Finite cell method for functionally graded materials based on V-models and homogenized microstructures

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Benjamin Wassermann ◽  
Nina Korshunova ◽  
Stefan Kollmannsberger ◽  
Ernst Rank ◽  
Gershon Elber
Keyword(s):  
Functionally Graded Materials ◽  
Large Scale ◽  
Functionally Graded ◽  
Material Behavior ◽  
Modeling Framework ◽  
Finite Cell Method ◽  
Geometric Framework ◽  
Graded Materials ◽  
Cell Method ◽  
Finite Cell

AbstractThis paper proposes an extension of the finite cell method (FCM) to V-rep models, a novel geometric framework for volumetric representations. This combination of an embedded domain approach (FCM) and a new modeling framework (V-rep) forms the basis for an efficient and accurate simulation of mechanical artifacts, which are not only characterized by complex shapes but also by their non-standard interior structure. These types of objects gain more and more interest in the context of the new design opportunities opened by additive manufacturing, in particular when graded or micro-structured material is applied. Two different types of functionally graded materials (FGM) are considered: The first one, multi-material FGM is described using the inherent property of V-rep models to assign different properties throughout the interior of a domain. The second, single-material FGM—which is heterogeneously micro-structured—characterizes the effective material behavior of representative volume elements by homogenization and performs large-scale simulations using the embedded domain approach.

scholarly journals Finite Cell Method for functionally graded materials based onV-models and homogenized microstructures

2020 ◽  
Author(s):  
Benjamin Wassermann ◽  
Nina Korshunova ◽  
Stefan Kollmannsberger ◽  
Ernst Rank ◽  
Gershon Elber
Keyword(s):  
Functionally Graded Materials ◽  
Large Scale ◽  
Functionally Graded ◽  
Material Behavior ◽  
Geometric Framework ◽  
Graded Materials ◽  
Cell Method ◽  
Complex Shapes ◽  
Large Scale Simulations ◽  
Single Material

Abstract This paper proposes an extension of the nite cell method (FCM) to V-rep models, a novel geometric framework for volumetric representations. This combination of an embedded domain approach (FCM) and a new modelingframework (V-rep) forms the basis for an efficient and accurate simulation of mechanical artifacts, which are not only characterized by complex shapes but also by their non-standard interior structure. These types of objects gain more and more interest in the context of the new design opportunities opened by additive manufacturing, in particular when graded or micro-structured material is applied. Two different types of functionally graded materials (FGM) are considered: The rst one, multi-material FGM is described using the inherent property of V-rep models to assign different properties throughout the interior of a domain. The second, single-material FGM { which is heterogeneously micro-structured { characterizes the effective material behavior of representative volume elements by homogenization and performs large-scale simulations using the embedded domain approach.

scholarly journals Finite Cell Method for functionally graded materials based on V-models and homogenized microstructures

2020 ◽  
Author(s):  
Benjamin Wassermann ◽  
Nina Korshunova ◽  
Stefan Kollmannsberger ◽  
Ernst Rank ◽  
Gershon Elber
Keyword(s):  
Functionally Graded Materials ◽  
Geometric Modeling ◽  
Geometric Model ◽  
Functionally Graded ◽  
Integration Scheme ◽  
Modeling Framework ◽  
Finite Cell Method ◽  
Graded Materials ◽  
Cell Method ◽  
Finite Cell

Abstract This paper proposes a computational methodology that allows a direct numerical simulation of heterogeneous/functionally graded materials based on V-reps/V-models and the Finite Cell Method (FCM). The FCM is an embedded domain approach that employs higher-order finite elements. The basic idea is to embed a complex geometric model into a fictitious domain that is trivial to mesh. The complexity of the geometry is then recaptured by an adapted precise numerical integration scheme for the elements cut by the boundary. For this, only a robust point inclusion test is required, which can be provided by various Computer-Aided Design (CAD) models. V-rep is a geometric modeling framework that represents the entire volume based on tri-variate B-Splines. Consequently, not only a point inclusion test is provided – but also the possibility to represent and model the interior domain. This allows to apply functionally graded material based on the tri-variate basis functions. These material parameters can then be regained during the simulation with an adapted point inclusion test. The potential of the proposed method especially in the context of additive manufacturing is demonstrated by several numerical examples.

Thermo-Elasto-Plastic Analysis of Thick-Walled Spherical Pressure Vessels Made of Functionally Graded Materials

2016 ◽  
Vol 08 (04) ◽  
pp. 1650054 ◽  
Author(s):  
Zeinab Mazarei ◽  
Mohammad Zamani Nejad ◽  
Amin Hadi
Keyword(s):  
Heat Flux ◽  
Functionally Graded Materials ◽  
Poisson’S Ratio ◽  
Pressure Vessels ◽  
Functionally Graded ◽  
Material Behavior ◽  
Poisson's Ratio ◽  
Uniform Heat Flux ◽  
Plastic Behavior ◽  
Graded Materials

An exact closed-form analytical solution is presented to solve the thermo-elasto-plastic problem of thick-walled spherical vessels made of functionally graded materials (FGMs). Assuming that the inner surface is exposed to a uniform heat flux, and that the outer surface is exposed to an airstream. The heat conduction equation for the one-dimensional problem in spherical coordinates is used to obtain temperature distribution in the sphere. Material properties are graded in the thickness direction according to a power law distribution, whereas the Poisson’s ratio is kept constant. The Poisson’s ratio due to slight variations in engineering materials is assumed constant. The plastic model is based on von Mises yield criterion and its associated flow rules under the assumption of perfectly plastic material behavior. For various values of inhomogeneity constant, the so-obtained solution is then used to study the distribution of limit heat flux, displacement and stresses versus the radial direction. Moreover, the effect of increasing the heat flux and pressure on the propagation of the plastic zone are investigated. Furthermore, the effect of change in Poisson’s ratio on the value of the critical material parameter is demonstrated. The present study is also validated by comparing the numerical results for thick elasto-plastic spherical shells available in the literature. To the best of the authors’ knowledge, in previous studies, exact thermo-elasto-plastic behavior of FGM thick-walled sphrical pressure vessels has not investigated.

scholarly journals Analysis of 2D heat conduction in nonlinear functionally graded materials using a local semi-analytical meshless method

2021 ◽  
Vol 6 (11) ◽  
pp. 12599-12618
Author(s):  
Chao Wang ◽  
◽  
Fajie Wang ◽  
Yanpeng Gong ◽  
◽  
...  
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Materials ◽  
Meshless Method ◽  
Large Scale ◽  
Heat Conduction Problem ◽  
Functionally Graded ◽  
Graded Materials ◽  
Kirchhoff Transformation ◽  
Graded Material ◽  
Equation Of Heat Conduction

<abstract> <p>This paper proposes a local semi-analytical meshless method for simulating heat conduction in nonlinear functionally graded materials. The governing equation of heat conduction problem in nonlinear functionally graded material is first transformed to an anisotropic modified Helmholtz equation by using the Kirchhoff transformation. Then, the local knot method (LKM) is employed to approximate the solution of the transformed equation. After that, the solution of the original nonlinear equation can be obtained by the inverse Kirchhoff transformation. The LKM is a recently proposed meshless approach. As a local semi-analytical meshless approach, it uses the non-singular general solution as the basis function and has the merits of simplicity, high accuracy, and easy-to-program. Compared with the traditional boundary knot method, the present scheme avoids an ill-conditioned system of equations, and is more suitable for large-scale simulations associated with complicated structures. Three benchmark numerical examples are provided to confirm the accuracy and validity of the proposed approach.</p> </abstract>

Dynamic Analysis with Stress Recovery for Functionally Graded Materials: Numerical Simulation and Experimental Benchmarking

2014 ◽  
Vol 2 (1) ◽  
pp. 21
Author(s):  
Carlos Alberto Dutra Fraga Filho ◽  
Fernando César Meira Menandro ◽  
Rivânia Hermógenes Paulino de Romero ◽  
Juan Sérgio Romero Saenz
Keyword(s):  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Stress Recovery ◽  
Graded Materials
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