ORBi Collection: Mechanical engineering
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Microstructural design using stress–based topology optimization
http://hdl.handle.net/2268/202710
Title: Microstructural design using stress–based topology optimization
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<br/>Author, co-author: Collet, Maxime; Bruggi, Matteo; Noël, Lise; Bauduin, Simon; Duysinx, Pierre
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<br/>Abstract: New additive manufacturing techniques break the limitations encountered for years when producing components descending from topology optimization. Classical design procedures focus on macro-structural optimization to sustain given loads but today innovative manufacturing processes allow considering structures exhibiting tailored microstructures, i.e. the well known microstructural design. The practical applications of structures including material design is mainly motivated by the greater performances that can be achieved compared to classical solutions. Microstructural design has been shown a great interest as attested by recent works. However, stress–based topology optimization has not yet been extensively exploited when addressing microstructural design using numerical homogenization though stress constraints is an important feature and have gained in interest in the field of topology optimization. This contribution investigates the problem of material design enforcing stress constraints within periodic microstructures by considering a representative volume element (RVE) subject to prescribed strain fields. The SIMP approach is adopted as material interpolation law while the optimization problems are solved using a sequential convex programming approach. In particular the well known method of moving asymptotes (MMA) is considered. Numerical homogenization is used to assess the effective elastic properties of the microstructures. The Von Mises stress criterion is used to impose the constraints on the stress level. This work discusses the formulation of a well-posed design problem as well as some numerical issues encountered. The developed solution procedure is first validated by comparison against analytical results, e.g. the single inclusion of Vigdergauz microstructure.Design of microstructures using stress-based topology optimization
http://hdl.handle.net/2268/202709
Title: Design of microstructures using stress-based topology optimization
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<br/>Author, co-author: Collet, Maxime; Bruggi, Matteo; Noël, Lise; Bauduin, Simon; Duysinx, Pierre
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<br/>Abstract: This paper aims at designing microstructures using stress-based topology optimization. Most of the developments so far have been made for compliance design in various field of applications as reflected in the literature. The emergence of the new additive manufacturing techniques allows to consider porous material, such as lattice structures for instance, which ca be used for the design of structural components subject to various solicitations. Those components must account for the stress level to prevent failure everywhere in the microstructures and by extension the whole structure itself. This work proposes to design such microstructures using topology optimization with limitation on the stress level within the microstructures before printing the result. The homogenization technique is used to determine the equivalent material properties. The issues and perspectives are also discussed.Probabilistic prediction of the quality factor of micro-resonator using a stochastic thermo-mechanical multi-scale approach
http://hdl.handle.net/2268/202510
Title: Probabilistic prediction of the quality factor of micro-resonator using a stochastic thermo-mechanical multi-scale approach
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<br/>Author, co-author: Wu, Ling; Lucas, Vincent; Golinval, Jean-Claude; Paquay, Stéphane; Noels, Ludovic
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<br/>Abstract: As the size of the device is only one or two orders of magnitude higher than the size of the grains, the structural properties, such as the thermo-elastic quality factor (Q), of micro-electro-mechanical systems (MEMS) made of poly-crystalline materials exhibit a scatter, due to the existing randomness in the grain size, grain orientation, surface roughness...
In order to predict the probabilistic behavior of micro-resonators, the authors extend herein a previously developed stochastic 3-scale approach [1] to the case of thermoelastic damping [2]. In this method, stochastic volume elements (SVEs) [3] are defined by considering random grain orientations in a tessellation. For each SVE realization, the mesoscopic apparent elasticity tensor, thermal conductivity tensor, and thermal dilatation tensor can be obtained using thermo-mechanical computational homogenization theory [4]. The extracted mesoscopic apparent properties tensors can then be used to define a spatially correlated meso-scale random field, which is in turn used as input for stochastic finite element simulations. As a result, the probabilistic distribution of the quality factor of micro-resonator can be extracted by considering Monte-Carlo simulations of coarse-meshed micro-resonators, accounting implicitly for the random micro-structure of the poly-silicon material.
[1] V. Lucas, J.-C. Golinval, S. Paquay, V.-D. Nguyen, L. Noels, L. Wu, A stochastic computational multiscale approach; Application to MEMS resonators. Computer Methods in Applied Mechanics and Engineering, 294, 141-167, 2015.
[2] L. Wu, V. Lucas, V.-D. Nguyen, J.-C. Golinval, S. Paquay, L. Noels, A Stochastic Multiscale Approach for the Modeling of Thermoelastic Damping in Micro-Resonators. Submitted.
[3] M. Ostoja-Starzewski, X.Wang, Stochastic finite elements as a bridge between random material microstructure and global response, Computer Methods in Applied Mechanics and Engineering, 168, 35--49, 1999.
[4] I. Özdemir, W. A. M. Brekelmans, M. G. D. Geers, Computational homogenization for heat conduction in heterogeneous solids, International Journal for Numerical Methods in Engineering 73, 185-204, 2008.A computational stochastic multiscale methodology for MEMS structures involving adhesive contact
http://hdl.handle.net/2268/202313
Title: A computational stochastic multiscale methodology for MEMS structures involving adhesive contact
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<br/>Author, co-author: Hoang Truong, Vinh; Wu, Ling; Paquay, Stéphane; Golinval, Jean-Claude; Arnst, Maarten; Noels, Ludovic
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<br/>Abstract: This work aims at developing a computational stochastic multiscale methodology to quantify the uncertainties of the adhesive contact problems due to capillary effects and van der Waals forces in MEMS. Because the magnitudes of the adhesive forces strongly depend on the surface interaction distances, which in turn evolve with the roughness of the contacting surfaces, the involved structural behaviors suffer from a scatter. To numerically predict the probabilistic behaviors of structures involving adhesion, the proposed method introduces stochastic meso-scale random apparent contact forces which can be integrated into a stochastic finite element model. Because the evaluation of their realizations is expensive, a generator for the random apparent contact force using the polynomial chaos expansion is constructed in an efficient way.Design of an experimental set-up to analyse compliant mechanisms used for the deployment of a panel
http://hdl.handle.net/2268/202229
Title: Design of an experimental set-up to analyse compliant mechanisms used for the deployment of a panel
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<br/>Author, co-author: Dewalque, Florence; Bruls, Olivier
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<br/>Abstract: Due to their high complexity, compliant mechanisms require high-ﬁdelity mechanical models to reach a detailed understanding of their characteristics and predict their actual behaviour in various situations. This work focuses on tape springs which are used as an alternative to common mechanisms composed of kinematic joints. They present several assets such as, among others, passive deployment and self-locking, but they are characterised by a highly nonlinear behaviour including buckling, the formation of folds and hysteresis. An experimental set-up is then designed to gather information on these phenomena, while in parallel an equivalent
ﬁnite element model is developed. Quasi-static and dynamic tests are performed, as well as small amplitude vibration tests and large amplitude deployments in order to collect data in a broad variety of cases. The post-processing of the numerous raw data shows, with the help of statistical considerations, the good quality of the acquisitions. Finally, the ﬁnite element model proves to be fairly well correlated to the experimental results.Level set optimization of bimaterial structures and microstructures considering stress and damage resistance
http://hdl.handle.net/2268/202226
Title: Level set optimization of bimaterial structures and microstructures considering stress and damage resistance
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<br/>Author, co-author: Noël, LiseTime-Varying Modal Parameters Identification in the Modal Domain
http://hdl.handle.net/2268/201971
Title: Time-Varying Modal Parameters Identification in the Modal Domain
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<br/>Author, co-author: Bertha, Mathieu; Golinval, Jean-ClaudeTwo 3D thermomechanical numerical models of friction stir welding processes with a trigonal pin
http://hdl.handle.net/2268/201925
Title: Two 3D thermomechanical numerical models of friction stir welding processes with a trigonal pin
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<br/>Author, co-author: Bussetta, Philippe; Feulvarch, Eric; Tongne, Amèvi; Boman, Romain; Bergheau, Jean-Michel; Ponthot, Jean-PhilippeOverhanging Constraints in Addivitive Manufacturing Using Two Different Tools
http://hdl.handle.net/2268/201827
Title: Overhanging Constraints in Addivitive Manufacturing Using Two Different Tools
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<br/>Author, co-author: Bauduin, Simon; Collet, Maxime; Duysinx, Pierre
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<br/>Abstract: Topology optimization is widely used as a design tool for advanced application in mechanical, aerospace and automotive industries. This technique offers an optimal distribution of a predetermined amount of material in a given design space. In the last years, a lot of efforts has been invested into the development of high performance methods such as homogenization, SIMP or BESO. However as the state of the art in manufacturing experiences evolution, a coupling between topology optimization and additive manufacturing is needed. Additive manufacturing has numerous advantages that fits the characteristics of topology optimized designs. It can manufacture highly complex design without high cost increase and furthermore continuous density material of the SIMP method could be manufactured by lattice structures. With all the opportunities given by the additive manufacturing the urge to bind the last one to topology optimization is heavily required. Specific constraints related to manufacturing issues have to be taken into account such as the need of supports structures to ensure a good heat evacuation during the manufacturing process, as well as to hold up overhanging section. Some researches have been done to try to include this constraint in the optimization problem such as Leary and al or Andrew T. Gaynor. However this work focuses on 2 different methods (projection scheme and mechanical approach) to tackle the overhanging problem and compare them .Overhanging Constraints in Addivitive Manufacturing Using Two Different Tools
http://hdl.handle.net/2268/201826
Title: Overhanging Constraints in Addivitive Manufacturing Using Two Different Tools
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<br/>Author, co-author: Bauduin, Simon; Collet, Maxime; Duysinx, Pierre
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<br/>Abstract: Topology optimization is widely used as a design tool for advanced application in mechanical, aerospace and automotive industries. This technique offers an optimal distribution of a predetermined amount of material in a given design space. In the last years, a lot of efforts has been invested into the development of high performance methods such as homogenization, SIMP or BESO. However as the state of the art in manufacturing experiences evolution, a coupling between topology optimization and additive manufacturing is needed. Additive manufacturing has numerous advantages that fits the characteristics of topology optimized designs. It can manufacture highly complex design without high cost increase and furthermore continuous density material of the SIMP method could be manufactured by lattice structures. With all the opportunities given by the additive manufacturing the urge to bind the last one to topology optimization is heavily required. Specific constraints related to manufacturing issues have to be taken into account such as the need of supports structures to ensure a good heat evacuation during the manufacturing process, as well as to hold up overhanging section. Some researches have been done to try to include this constraint in the optimization problem such as Leary and al or Andrew T. Gaynor. However this work focuses on 2 different methods (projection scheme and mechanical approach) to tackle the overhanging problem and compare them .Stochastic multi-scale modelling of MEMS
http://hdl.handle.net/2268/201815
Title: Stochastic multi-scale modelling of MEMS
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<br/>Author, co-author: Lucas, Vincent
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<br/>Abstract: When studying Micro-Electro-Mechanical Systems (or MEMS) made of poly-crystalline materials, as the size of the device is only one or two orders of magnitude higher than the size of the grains, the structural properties exhibit a scatter at the macro-scale due to the existing randomness in the grain size, grain orientation, surface roughness... In order to predict the probabilistic behaviour at the structural scale, we investigated the recourse to a stochastic 3-scale approach in this thesis dissertation.
Estimating the scatter in the response of the structure is studied at macro-scale based on stochastic finite elements along with Monte-Carlo simulations. To produce accurate results, the mesh size of the finite element approach should be small enough so that the heterogeneities can be captured. This can lead to overwhelming computation if the microstructure is directly considered, thus justifying the recourse to stochastic homogenisation to define a meso-scale random field. Based on a stochastic model of this random field, the variability of the response of the structure can be computed.
In this work, the micro-scale uncertainties are modelled based on measurements provided by the IMT-Bucharest institute. These uncertainties are then propagated towards the macro-scale for 3 different problems. The first one serves the purpose of verification. The variability of the resonance frequency of a micro-beam is computed and compared to a reference numerical solution. The second problem extends the 3-scale approach to the thermo-elastic case. Thus the uncertainties of the quality factor of 3D beams are studied with a modelling of the anchor. Finally, the third problem aims at propagating surface roughness uncertainties on the resonance frequency of thin plates.New computational method of the ball/race contacts transverse loads of high speed ball bearings without race control hypothesis
http://hdl.handle.net/2268/201686
Title: New computational method of the ball/race contacts transverse loads of high speed ball bearings without race control hypothesis
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<br/>Author, co-author: Servais, Christophe; Bozet, Jean-LucUnified treatment of microscopic boundary conditions in computational homogenization method for multiphysics problems
http://hdl.handle.net/2268/201685
Title: Unified treatment of microscopic boundary conditions in computational homogenization method for multiphysics problems
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<br/>Author, co-author: Nguyen, Van Dung; Wu, Ling; Homsi, Lina; Noels, Ludovic
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<br/>Abstract: Computational homogenization (so-called FE2) method is an effective tool to model complex behavior of heterogeneous media allowing direct coupling between the structure response and the evolving microstructure not only in purely mechanical problems but also in multiphysics problems [1]. The basic idea of this method is to obtain the macroscopic constitutive relationships from the resolution of the microscopic boundary value problem (BVP) defined on a representative volume element. This method does not requires any constitutive assumption at the macroscopic level, but an appropriate microscopic boundary condition has to be defined. Our work focuses on the unified treatment of the microscopic boundary condition in a multiphysics microscopic BVP. In particular, an efficient way to compute the tangent operator is developed for an arbitrary kind of boundary conditions.
When considering the FE2method, the homogenized stresses and homogenized tangents at every macroscopic integration points are required. From the energy consistency condition between macroscopic and microscopic problems, the homogenized stresses can be easily computed by the volumetric averaging integrals of the microscopic counterparts. The required homogenized tangents often follows a stiffness condensation from the microscopic stiffness matrix at the equilibrium state [2]. When using the stiffness condensation, the microscopic stiffness matrix needs to be partitioned, and dense matrices based on Schur complements (under a matrix form 𝐊̃ 𝑏𝑏=𝐊𝑏𝑏−𝐊𝑏𝑖𝐊𝑖𝑖−1𝐊𝑖𝑏) have to be estimated. The matrix operations based on Schur complements require a large time consuming and a lot of memory when increasing the number of degrees of freedom of the microscopic BVPs. This work proposes an efficient method allowing to compute the homogenized tangents without significant effort. The microscopic stiffness matrix does not need to be partitioned. The homogenized tangents are computed by solving a linear system, which is based on the linearized system at the converge solution of the microscopic BVP, with multiple right hand sides.
With proposed numerical improvements, the FE2 method is used in a fully thermo-mechanically-coupled simulation. The temperature-dependent elastoplastic behavior, thermal conduction as well as the heat conversion from the mechanical deformation are considered in the hyperelastic large strain framework.
[1]. Geers, M. G. D., Kouznetsova, V. G., Brekelmans, W. A. M., 2010. J. Comput. Appl. Math. 234 (7), 2175-2182.
[2]. Kouznetsova, V., Brekelmans, W. A. M., Baaijens, F. P. T., 2001. Comput. Mech. 27 (1), 37-48.A coupled electro-thermo-mechanical discontinuous Galerkin method applied on composite materials
http://hdl.handle.net/2268/201684
Title: A coupled electro-thermo-mechanical discontinuous Galerkin method applied on composite materials
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<br/>Author, co-author: Homsi, Lina; Noels, Ludovic
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<br/>Abstract: Carbon fiber reinforced polymer composites have become increasingly important due to their unique properties which are appreciated in many practical applications such as low weight, low cost, low density, high mechanical characteristics. Moreover the range of their electrical conductivity can be controlled by the amount of carbon fibers. Carbon fiber reinforced polymer composites consist of at least two components, a polymer matrix (generally dielectric) and electrically conductive fillers. This combination results in multifunctional composites, both structural and conductive. The existence of the polymer matrix will avoid catastrophic failure due to fiber breaking, and the existence of the carbon fibers will enhance strength and stiffness on one hand, and will allow to a significant temperature gradient when electric current is applied on the other hand. The objective of this paper is to study the response of the carbon fiber reinforced polymer composites when an electric power is applied and to determine the effective properties. To this end governing equations describing electro-thermo-mechanical coupling in composite materials are developed and discretized using the Discontinuous Galerkin (DG) finite element method. DG methods have many advantages such as optimal convergence and local approximation properties in addition to their flexibility for mesh adaption and their straightforward use of high order polynomial approximations. A micromechanical model of unidirectional carbon fibers dispersed in a polymer matrix is formulated considering the interaction of electrical, thermal and mechanical fields It is then solved using the DG method to determine the time dependent response of the electro-thermo-mechanical coupling and quantify the variation of the fields.Simulations of composite laminates inter and intra-laminar failure using on a non-local mean-field damage-enhanced multi-scale method
http://hdl.handle.net/2268/201678
Title: Simulations of composite laminates inter and intra-laminar failure using on a non-local mean-field damage-enhanced multi-scale method
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<br/>Author, co-author: Wu, Ling; Adam, Laurent; Bidaine, Benoît; Noels, Ludovic
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<br/>Abstract: The failure of carbon fiber reinforced composite laminates is studied using a multiscale method.
A non-local mean-field homogenization (MFH) method accounting for the damage evolution of the matrix phase of the composite material [1] is considered in each ply in order to capture the intra-laminar failure. In that formulation, an incremental-secant MFH approach is used to account for the elastic unloading of the fibers during the strain softening of the matrix. In order to avoid the strain/damage localization caused by the matrix material softening, the damage enhanced MFH was formulated in an implicit non-local way [2]. Accurate predictions of the composite softening behavior and of the different phases response is then achieved. The delamination process is modeled by recourse to a hybrid discontinuous Galerkin (DG)/ extrinsic cohesive law approach.
An open-hole composite laminate with a quasi-isotropic sequence ([90/45/-45/90/0]S) is then studied experimentally and using the multiscale method [3]. The numerical model is found to predict the damage bands along the fiber directions in agreement with the experimental samples inspected by X-ray computed tomography (XCT). Moreover, the predicted delamination pattern is found to match the experimental observations.
Finally, with a view to stochastic analysis, the effect of the volume fraction and orientation variations on the failure is studied by defining them as random variables.
REFERENCES
[1] L. Wu, L. Noels, L. Adam, I. Doghri, An implicit-gradient-enhanced incremental-secant mean- field homogenization scheme for elasto-plastic composites with damage, International Journal of Solids and Structures, 50, 3843-3860, 2013.
[2] R. Peerlings, R. de Borst, W. Brekelmans, S. Ayyapureddi, Gradient-enhanced damage for quasi-brittle materials. International Journal for Numerical Methods in Engineering, 39, 3391-3403, 1996.
[3] L. Wu, F. Sket, J.M. Molina-Aldareguia, A. Makradi, L. Adam, I. Doghri, L. Noels, A study of composite laminates failure using an anisotropic gradient-enhanced damage mean-field homogenization model, Composite Structures, 126, 246–264, 2015.A principle of similarity for nonlinear vibration absorbers
http://hdl.handle.net/2268/201300
Title: A principle of similarity for nonlinear vibration absorbers
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<br/>Author, co-author: Habib, Giuseppe; Kerschen, Gaëtan
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<br/>Abstract: This paper develops a principle of similarity for the design of a nonlinear absorber, the nonlinear tuned vibration absorber (NLTVA), attached to a nonlinear primary system. Specifically, for effective vibration mitigation, we show that the NLTVA should feature a nonlinearity possessing the same mathematical form as that of the primary system. A compact analytical formula for the nonlinear coefficient of the absorber is then derived. The formula, valid for any polynomial nonlinearity in the primary system, is found to depend only on the mass ratio and on the nonlinear coefficient of the primary system. When the primary system comprises several polynomial nonlinearities, we demonstrate that the NLTVA obeys a principle of additivity, i.e., each nonlinear coefficient can be calculated independently of the other nonlinear coefficients using the proposed formula.Passive linearization of nonlinear resonances
http://hdl.handle.net/2268/201299
Title: Passive linearization of nonlinear resonances
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<br/>Author, co-author: Habib, Giuseppe; Grappasonni, Chiara; Kerschen, Gaëtan
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<br/>Abstract: The objective of this paper is to demonstrate that the addition of properly-tuned nonlinearities to a nonlinear system can increase the range over which a speci c resonance responds linearly. Speci cally, we seek to enforce two important properties of linear systems, namely the force-displacement proportionality and the invariance of resonance frequencies. Numerical simulations and experiments are used to validate the theoretical ndings.Passive Linearization of Nonlinear System Resonances
http://hdl.handle.net/2268/201298
Title: Passive Linearization of Nonlinear System Resonances
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<br/>Author, co-author: Habib, Giuseppe; Grappasonni, Chiara; Kerschen, Gaëtan
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<br/>Abstract: In this work we demonstrate that the addition of properly-tuned nonlinearities to a nonlinear system can increase the range over which a specific resonance responds linearly. Specifically, we seek to enforce two important properties of linear systems, namely the force-displacement proportionality and the invariance of resonance frequencies. Theoretical findings are validated through numerical simulations and experiments.A Stochastic Multi-Scale Approach for the Modeling of Thermo-Elastic Damping in Micro-Resonators
http://hdl.handle.net/2268/201256
Title: A Stochastic Multi-Scale Approach for the Modeling of Thermo-Elastic Damping in Micro-Resonators
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<br/>Author, co-author: Wu, Ling; Lucas, Vincent; Nguyen, Van Dung; Golinval, Jean-Claude; Paquay, Stéphane; Noels, Ludovic
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<br/>Abstract: The aim of this work is to study the thermo-elastic quality factor (Q) of micro-resonators with a stochastic multi-scale approach. In the design of high-Q micro-resonators, thermo-elastic damping is one of the major dissipation mechanisms, which may have detrimental effects on the quality factor, and has to be predicted accurately. Since material uncertainties are inherent to and unavoidable in micro-electromechanical systems (MEMS), the effects of those variations have to be considered in the modeling in order to ensure the required MEMS performance. To this end, a coupled thermo-mechanical stochastic multi-scale approach is developed in this paper. Thermo-mechanical micro-models of polycrystalline materials are used to represent micro-structure realizations. A computational homogenization procedure is then applied on these statistical
volume elements to obtain the stochastic characterizations of the elasticity tensor, thermal expansion, and conductivity tensors at the meso-scale. Spatially correlated meso-scale random fields can thus be generated to represent the stochastic behavior of the homogenized material properties. Finally, the distribution of the thermo-elastic quality factor of MEMS resonators is studied through a stochastic finite element method using as input the generated stochastic random field.Embedded solids of any dimension in the X-FEM defined on higher-order approximations
http://hdl.handle.net/2268/201087
Title: Embedded solids of any dimension in the X-FEM defined on higher-order approximations
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<br/>Author, co-author: Duboeuf, Frédéric; Béchet, Eric
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<br/>Abstract: Embedded interface methods bring a significant simplification of the modelling process before analysis. Complex geometries and moving boundaries may be described with great flexibility, reducing the meshing step to that of a simple bounding box. Following this idea – to dissociate the field approximation from the geometric description – manifolds of different dimensions may be embedded in the same bulk mesh. However, special attention should be given to the difference of dimensions between that of problem domain and that of bulk mesh (the codimension).
Whereas the direct use of the shape functions of the bulk mesh is possible for a problem domain of codimension zero, this approach is no longer possible in other configurations, for instance a beam in a 3D mesh. Unlike approaches introducing independent overlapping meshes for each subdomain, function spaces may be built from the traces of higher dimensional spaces built upon the bulk mesh. For closed curves in 2D and closed surfaces in 3D, the resulting discrete method based on P1 FE have already been studied in the literature. To avoid badly conditioned linear systems, specific treatments are required, e.g. preconditioning approaches or stabilization techniques. Here, we propose to deplete wisely the trace space.
We investigate higher-order function spaces to solve the diffusion equation in embedded solids of any codimension. A new space-reducer algorithm is introduced to design the dedicated spaces that avoids ill-conditionning while treating boundary conditions. We present the results of several numerical experiments with convergence analyses. To conclude, applications of this technique to embedded beams or shells is discussed.