ORBi Collection: Mechanical engineering
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Trajectory optimization for 3D robots with elastic links
http://hdl.handle.net/2268/184353
Title: Trajectory optimization for 3D robots with elastic links
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<br/>Author, co-author: Lismonde, Arthur; Sonneville, Valentin; Bruls, OlivierA level set approach for the structural optimization of flexible mechanisms
http://hdl.handle.net/2268/184303
Title: A level set approach for the structural optimization of flexible mechanisms
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<br/>Author, co-author: Tromme, Emmanuel; Tortorelli, Daniel; Bruls, Olivier; Duysinx, Pierre
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<br/>Abstract: With the evolution of virtual prototyping, mechanical systems are commonly analyzed using a multibody system (MBS) approach to study the behavior of the entire system and notably the dynamic interactions between the components.
Modern structural optimization of mechanical systems considers the dynamic loading exerted on the individual flexible components. The consideration is an essential feature and can be implemented in two ways. Firstly, one can consider a strong coupling wherein the component’s optimization is performed using the time dependent loading conditions coming directly from the MBS simulation. Secondly, one can consider a weak coupling wherein the component’s optimization is performed using a series of static load cases that do not fully account for the interactions between the components of the MBS. Rather this approach performs a MBS simulation to evaluate the loads for the initial design and then optimizes the component assuming the loads do not change. The process of evaluating the loads and then performing the optimization is repeated until suitable convergence criteria is satisfied, assuming convergence is possible.
The present paper focuses on the strong coupling method wherein the flexible MBS dynamic analysis is based on a nonlinear finite element formalism [1]. A level set (LS) description of the component geometry is used to enable a generalized shape optimization. The LS approach combines the advantages of shape and topology optimizations. Moreover, since the component boundaries are defined by CAD features, the manufacturing process is facilitated as no post-processing step of a rasterized design is required. The design sensitivity analysis for MBS is revisited in order to facilitate its implementation. The optimization of a slider-crank mechanism and a 2-dof robot is provided to exemplify the procedure.
[1] Géradin M., Cardona A. (2001) Flexible Multibody Dynamics: A Finite Element Approach. John Wiley & Sons, New York.A viscoelastic-viscoplastic-damage constitutive model based on a large strain hyperelastic formulation for amorphous glassy polymers
http://hdl.handle.net/2268/184286
Title: A viscoelastic-viscoplastic-damage constitutive model based on a large strain hyperelastic formulation for amorphous glassy polymers
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<br/>Author, co-author: Nguyen, Van Dung; Morelle, Xavier; Lani, Frédéric; Pardoen, Thomas; Bailly, Christian; Noels, Ludovic
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<br/>Abstract: The aim of this work is to develop an efficient large-strain hyperelastic constitutive model for amorphous polymers in the glassy state. These materials exhibit a complex rate- and pressure-sensible behavior in both elastic and plastic regimes. After an initial linear elastic region, a nonlinear stage continues until reaching a peak stress, which is followed by a softening stage. At large strains, when the softening is saturated, a re-hardening stage is reached. The viscoelastic effect is captured using the generalized Maxwell model. The viscoplastic effect is considered using a Perzyna-type flow rule incorporating a pressure sensitive yield surface and a non-associated flow potential. This yield surface is extended from the Drucker-Prager one. The saturated softening phenomenon is modelled using an isotropic numerical damage variable progressed by a saturated softening law. With the introduction of the damage parameter, a non-local implicit gradient damage model is used to avoid the loss of the solution uniqueness. Through experimental comparisons, it is shown that the proposed model has the ability to model the complex mechanical responses of amorphous glassy polymers.A Non-Local Damage-Enhanced Incremental-Secant Mean-Field-Homogenization For Composite Laminate Failure Predictions
http://hdl.handle.net/2268/184285
Title: A Non-Local Damage-Enhanced Incremental-Secant Mean-Field-Homogenization For Composite Laminate Failure Predictions
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<br/>Author, co-author: Wu, Ling; Adam, Laurent; Doghri, Issam; Noels, Ludovic
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<br/>Abstract: Recently, the authors have presented an incremental-secant mean-field homogenisation (MFH) process for non-linear composite materials [4]. In this formulation, a virtual elastic unloading
is applied to evaluate the virtual residual stress and strain states reached in each elasto-plastic
phase. These virtual states are then used as a starting point to apply a secant homogenization
method. This incremental-secant MFH process can handle non-proportional and nonmonotonic
loadings, and naturally possesses an isotropic instantaneous stiffness operator to
be used in the Eshelby tensor. This incremental-secant MFH homogenization can account for the first and second statistical moment estimation of the current yield stress in the composite phases during the computation of the plastic flow. When accounting for a second statistical moment estimation, the plastic yield in the composite material phases is captured with a higher accuracy, improving the predictions, mainly in the case of short fiber composite materials [6], see Fig. 1(a). The incremental MFH can handle material softening when extended to include a damage model. Indeed, as the secant formulation is applied from an unloaded state, the inclusion phase can be elastically unloaded during the softening of the matrix phase, contrarily to the case of the incremental-tangent method [3, 5], see Fig. 1(b). Moreover, when formulating the damage model in the composite phases in a non-local way, as with the non-local implicit approach, [1, 2], the MFH scheme can be used to model strain localization in composite structures [5], without suffering from the loss of the solution uniqueness.A probabilistic multi-scale model for polycrystalline MEMS resonators
http://hdl.handle.net/2268/184284
Title: A probabilistic multi-scale model for polycrystalline MEMS resonators
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<br/>Author, co-author: Lucas, Vincent; Wu, Ling; Paquay, Stéphane; Golinval, Jean-Claude; Noels, Ludovic
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<br/>Abstract: The size of micro-electro-mechanical systems (MEMS) is only one or two orders of magnitude higher than the size of their micro-structure, i.e. their grain size. As a result, the structural properties exhibit a scatter. As an example we study the beam resonator illustrated in Fig. 1(a), made of poly-silicon material, in which each grain has a random orientation. Solving the problem with a full direct numerical simulation combined to a Monte-Carlo method allows the
probability density function to be computed as illustrated in Fig. 1(b). However this methodology
is computationally expensive due to the number of degrees of freedom required to study one sample, motivating the development of a non-deterministic 3-scale approach [3]. In a multiscale approach, at each macro-point of the macro-structure, the resolution of a microscale
boundary value problem relates the macro-stress tensor to the macro-strain tensor. At the micro-level, the macro-point is viewed as the center of a Representative Volume Element (RVE). The resolution of the micro-scale boundary problem can be performed using finite-element simulations, as in the computational homogenization framework, e.g. [2]. However,
to be representative, the micro-volume-element should have a size much bigger than the microstructure size.
In the context of the MEMS resonator, this representativity is lost and Statistical Volume Elements (SVE) are considered. These SVEs are generated under the form of a Voronoi tessellation with a random orientation for each silicon grain. Hence, a Monte-Carlo procedure
combined with a homogenization technique allows a distribution of the material tensor at the
meso-scale to be estimated. The correlation between the meso-scale material tensors of two
SVEs separated by a given distance can also be evaluated.
A generator at the meso-scale based on the spectral method [4] is implemented. The generator
[3] accounts for a lower bound [1] of the meso-scale material tensor in order to ensure the
existence of the second-order moment of the Frobenius norm of the generated material tensor
inverse [5].
Using the random meso-scale field obtained with the meso-scale generator, which accounts
for the spatial correlation, a Monte-Carlo method can be used at the macro-scale to predict the
probabilistic behavior of the MEMS resonator.Damage process sensitivity analysis using an XFEM-Level Set framework
http://hdl.handle.net/2268/184010
Title: Damage process sensitivity analysis using an XFEM-Level Set framework
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<br/>Author, co-author: Noël, Lise; Duysinx, Pierre; Maute, Kurt
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<br/>Abstract: Designing efficient and lightweight structures is a key objective for many industrial applications such as in aerospace or the automotive industry. To this end, composite materials are appealing as they combine high stiffness and light weight. The main challenge slowing down the integration of such materials in real structures is their damage be- havior. The latter should be considered in the design process of the structures. This work focuses on developing a systematic approach to designing structures that can sustain an acceptable amount of degradation or exhibit a low sensitivity to damage. An optimization approach is chosen to achieve this goal. To deal with complex geometries and to allow for large shape modifications in the optimization process, the extended finite element method (XFEM) is advantageously combined with a level set description of geometry. The degradation of materials is modeled by using a non-local damage model, motivated by the work of James and Waisman on a density approach to topol- ogy optimization. To solve design problems with damage constraints by gradient-based optimization method, a sensitivity analysis of the damage process is developed. Damage propagation and growth is an irreversible pro- cess. Therefore, the path dependence of the structural response needs to be accounted for in the sensitivity analysis. In this paper, we present an analytical approach for efficiently and accurately evaluating the design sensitivities, considering both direct and adjoint formulations. Finally, the sensitivity analysis approach is studied with simple benchmark problems and compared with the results obtained by finite differences.Electrical tuned vibration absorber: application of the equal-peak method to linear and non-linear RL piezoelectric shunts
http://hdl.handle.net/2268/184003
Title: Electrical tuned vibration absorber: application of the equal-peak method to linear and non-linear RL piezoelectric shunts
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<br/>Author, co-author: TONDREAU, Gilles; DERAEMAEKER, Arnaud; Soltani, Payam; Kerschen, GaëtanDeterministic Manufacturing constraints for Optimal Distribution in the Case of Additive Manufacturing
http://hdl.handle.net/2268/183981
Title: Deterministic Manufacturing constraints for Optimal Distribution in the Case of Additive Manufacturing
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<br/>Author, co-author: Bauduin, Simon; Collet, Maxime; Duysinx, Pierre
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<br/>Abstract: An overview of the difficulties of coupling additive manufacturing to topology optimization with various solution founded and implemented.Shape optimization of bimaterial (micro)structures using XFEM and a level set description
http://hdl.handle.net/2268/183980
Title: Shape optimization of bimaterial (micro)structures using XFEM and a level set description
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<br/>Author, co-author: Noël, Lise; Duysinx, Pierre
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<br/>Abstract: This work focuses on the problem of finding the optimal microstructural design for a material to suit particular applications. For this purpose, an analysis method was developed and implemented to get the response of bimaterial structures. The analysis is based on the two following methods:
• The level set description is used to represent the geometries of the (micro)structures, which can be rather complex. It allows to handle conveniently large shape modifications, which are often encountered in optimization process.
• The extended finite element method (XFEM) allows circumventing the conform meshing of the (micro)structures. This is really advantageous for optimization applications, since a fixed mesh can be used throughout the simulations.
To perform shape optimization, a sensitivity analysis of the design variables is needed. Fol- lowing the work by Van Miegroet (2007), an analytical approach to the computation of the derivatives has been developed. The stiffness matrix derivative is computed analytically starting from its discretized expression. Then, the expression of the stiffness matrix derivative is used to evaluate the sensitivity of various objective functions such as the compliance (global) or the stresses (local).
The analytical sensitivity analysis is tested on simple examples, based on small scale struc- tures. Then, it is validated against other sensitivity approaches: a finite difference approach, a semi-analytical approach,... Finally, the analytical sensitivity analysis is illustrated by solving classic academic shape optimization problems.Sensitivity analysis with the extended finite element method on bimaterial structures
http://hdl.handle.net/2268/183979
Title: Sensitivity analysis with the extended finite element method on bimaterial structures
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<br/>Author, co-author: Noël, Lise; Duysinx, Pierre
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<br/>Abstract: Material tailoring can be formulated as a structural optimization problem. To design com- posite microstructures, which can exhibit very complex geometries, a level set description is used to efficiently represent the microstructures. Fixed mesh methods and non conforming finite el- ement approximations, such as the extended finite element method (XFEM), presents several advantages to solve these problems of optimal material design.
The key issue to solve an optimization problem is to perform an accurate sensitivity analysis. Recently, van Miegroet et Duysinx (2007) developed a semi-analytical procedure to achieve shape optimization using XFEM on void-material structures. The shape is represented by a level set function, whose parameters are considered as design variables. The optimization problem is solved by applying mathematical programming algorithms. To realize material tailoring, we extend this work to be able to deal with bimaterial structures.
Working on void-material structures, the finite element approximation on a partially or on a fully filled element remains the same and the number of degrees of freedom does not change either. These characteristics of the approximation slightly ease the derivation procedure. A valid sensitivity analysis can be performed implementing a semi-analytical method based on a finite element computation of the stiffness matrix derivative. Dealing with material-material interfaces, the approximations and the number of degrees of freedom associated to an element filled with only one material or an element filled with two different materials are different. A new approach, adapted to the bimaterial framework, to achieve the sensitivity analysis is needed.
To circumvent the problems linked to a finite difference computation, an analytical method is developed to perform the sensitivity analysis. Several other method, just like the global finite dif- ference, the semi-analytical computation, ... are also implemented to evaluate the performance and the validity of the analytical method.
The developments are illustrated on academic test cases. Those are designed so that all the possible pathologic cases arise. The performance osf each method can then be easily evaluated. Finally, the analytical method is used in a simple optimization problem, where the shape of a solid inclusion is optimized to reach minimal compliance.A ROBUST APPROACH OF TOPOLOGIC OPTIMIZATION OF MECHANICAL AND AERONAUTICAL COMPONENTS FABRICATED BY ADDITIVE MANUFACTURING
http://hdl.handle.net/2268/183894
Title: A ROBUST APPROACH OF TOPOLOGIC OPTIMIZATION OF MECHANICAL AND AERONAUTICAL COMPONENTS FABRICATED BY ADDITIVE MANUFACTURING
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<br/>Author, co-author: Bauduin, SimonPoster: CONTRIBUTIONS TO TOPOLOGY OPTIMIZATION OF STRUCTURAL COMPONENTSMADE BY ADDITIVEMANUFACTURING
http://hdl.handle.net/2268/183891
Title: Poster: CONTRIBUTIONS TO TOPOLOGY OPTIMIZATION OF STRUCTURAL COMPONENTSMADE BY ADDITIVEMANUFACTURING
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<br/>Author, co-author: Collet, MaximeTopology optimization of mechanical and aerospace components subject to fatigue stress constraints
http://hdl.handle.net/2268/183845
Title: Topology optimization of mechanical and aerospace components subject to fatigue stress constraints
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<br/>Author, co-author: Duysinx, Pierre; Collet, Maxime; Bauduin, Simon; Tromme, Emmanuel; Noël, Lise; Bruggi, Matteo
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<br/>Abstract: While topology optimization has been based mostly on compliance type formulations, industrial applications call for more elaborated formulations including several restrictions on the local displacements and the stress constraints in some critical zones. Topology optimization with stress constraints was initially considered in Duysinx & Bendsoe (1998). Later the stress constraint formulation was further extended to consider non equal stress constraints limits Bruggi & Duysinx (2012) and to improve the solution efficiency using different strategies such as global stress constraint formulations (Duysinx & Sigmund, 1998, Le et al. 2010). In the present work, the authors are investigating the formulations of stress constraint topology optimization to support the redesign of structural components that have to be fabricated using additive manufacturing. In this perspective, design problem requirements include tackling fatigue constraints during stress constrained topology optimization.
The work investigates different formulations of fatigue resistance which could be appropriate in a topology approach. At first the classical approach of mechanical engineering based on SN curves and Goodman or Soderberg lines. The treatment of these fatigue restrictions can take advantage of former work developed for unequal stress constraints by considering mean and alternating components of the stress state. In a second step our research is now focussing on more complex situations (3D stress states) which require resorting to more advanced criteria. Dang Van fatigue theory (Dang Van, Griveau, Message, 1989) has been selected but calls for a more elaborated procedure that is currently validated. Topology optimized structural layouts predicted using classical stress criteria, Goodman and Dang Van theories are compared.Stress constrained topology optimization for additive manufacturing: Specific character and solution aspects
http://hdl.handle.net/2268/183826
Title: Stress constrained topology optimization for additive manufacturing: Specific character and solution aspects
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<br/>Author, co-author: Duysinx, Pierre
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<br/>Abstract: Since the fundamental work by Bendsøe and Kikuchi (1988), topology optimization has been based on compliance type formulations (Bendsoe & Sigmund, 2003) while the number of works considering stress constraints are rather limited (Duysinx & Bendsoe, 1998). More recently the generalized shape optimization approach using level set methods (see for instance Allaire, Jouve, Troader, 2004, Belytchko, Xiao, Parimi, 2003) has followed the tracks of topology optimization and has mainly been focusing on compliance minimization problems.
The ‘compliance type’ formulation has produced quite interesting results in many problems because controlling the energy and the displacements under the loads is generally favourable for deflection control and because, for one load case, the compliance minimization leads to a fully stressed design nearly everywhere in the structure. However there are theoretical results that clearly show that the strongest and the stiffest structural layout can be quite different. As demonstrated in Rozvany & Birker (1994) truss topology optimization can lead to different results when there are several load cases, different stress limits in tension and compression, or when there are several materials involved.
Therefore, the first goal of the paper points out the importance of considering stress constraints as soon as the preliminary design phase, that is, to include stress constraints in the topology optimization problem. Revisiting some contributions of the authors, this paper aims at illustrating the key role of stress constraints in the framework of topology optimization of continuum structures. The recent developments are able to treat:
• Integrated stress criteria (i.e. global) relaxed stress constraints that aggregate the stress constraints in each finite element in order to be able to circumvent the large scale character of the local stress constraints.
• Stress criteria that are able to tackle non equal stress limits in tension and compression. The usual von Mises criterion is unable to predict real-life designs when the structure is made of materials with unequal stress limits like concrete or composite materials. These different behaviours in tension and compression result in quite specific designs.
Numerical applications make possible to point out the different nature of structural lay out for maximum strength and maximum stiffness. This one is clearly demonstrated in two kinds of particular situations: once several load cases are considered and when unequal stress limits in tension and compression are involved.
The second contribution of the paper deals with the solution aspects of large scale constrained optimization problems. Because of the huge number of design variables, dual methods combined with local convex approximations such as CONLIN (Fleury, 1989) or MMA (Svanberg, 1987) are well indicated to solve classical topology optimization methods. However stress constrained problems introduce also a so large number of active constraints that one comes to a rather delicate situation. We show that the optimizer effort increases mostly as the cube of the number of constraints. In order to circumvent the problem, the idea developed in the paper is to combine first or second order approximations (Bruyneel, Duysinx, Fleury, 2002) with zero order approximations of stress constraints, especially for the subset of restrictions that are likely not to be active or not to change too fast. At first the paper presents the way to derive zero-order approximations of -relaxed stress constraints (that is necessary to cope with the singularity phenomenon of stress constraints in topology optimization). Then the proposed hybrid approach mixing approximation of different orders is benchmarked on numerical applications illustrating the reduction of computation time for solving optimization problems without sacrifying to the robustness and efficiency.
Numerical applications will investigate topology optimized benchmark examples combined with additive manufacturing fabrication to illustrate the developments.Proceedings of the Ninth International Conference on System Simulation in Buildings - SSB 2014
http://hdl.handle.net/2268/183783
Title: Proceedings of the Ninth International Conference on System Simulation in Buildings - SSB 2014
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<br/>Abstract: This 9th International Conference on System Simulation in Buildings has been the opportunity
to gather researchers coming from 13 countries, sharing the last results of their research works.
Some of the presented works were conducted in the frame of projects from the International
Energy Agency’s Energy in Buildings and Communities Programme (EBC).
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<br/>Commentary: ISBN : 978-2-930772-10-3Numerical simulation of CAD thin structures using the eXtended Finite Element Method and Level Sets
http://hdl.handle.net/2268/183723
Title: Numerical simulation of CAD thin structures using the eXtended Finite Element Method and Level Sets
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<br/>Author, co-author: Legrain, Grégory; Geuzaine, Christophe; Remacle, Jean-François; Moës, Nicolas; Cresta, P.; Gaudin, J.Optimal design of flexible mechanisms using the Equivalent Static Load method and a Lie group formalism
http://hdl.handle.net/2268/183682
Title: Optimal design of flexible mechanisms using the Equivalent Static Load method and a Lie group formalism
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<br/>Author, co-author: Tromme, Emmanuel; Sonneville, Valentin; Bruls, Olivier; Duysinx, PierreTowards a predictive modelling of the normal and pathological gait
http://hdl.handle.net/2268/183673
Title: Towards a predictive modelling of the normal and pathological gait
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<br/>Author, co-author: Van Hulle, Romain; Schwartz, Cédric; Croisier, Jean-Louis; Denoël, Vincent; Forthomme, Bénédicte; Bruls, OlivierDetermination of Stress and Strain Fields in Cast and Heat Treated Bimetallic Rolling Mill Rolls
http://hdl.handle.net/2268/183155
Title: Determination of Stress and Strain Fields in Cast and Heat Treated Bimetallic Rolling Mill Rolls
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<br/>Author, co-author: Neira Torres, Ingrid; Tchuindjang, Jérôme Tchoufack; Sinnaeve, Mario; Flores, P.; Lecomte-Beckers, Jacqueline; Habraken, Anne
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<br/>Abstract: Efficient work rolls for Hot Strip mill roughing stands are usually produced as bimetallic spun cast rolls with a core material made of Spheroidal Graphite Iron (SGI) and a shell material made of High Chromium Steel alloy, semi-High speed steel or adapted High Speed steel chemistry. In this paper, the evolution of stress fields and microstructure during post casting cooling and subsequent heat treatment of a standard high chromium steel is targeted. This knowledge is a first step to analyze the different events that could happen during these production stages and provides the residual stress fields as well as the final roll microstructure which are interesting data for roll service life. As far as roughing mill work rolls for roughing mills are concerned, current trends in terms of work roll design are forcing the roll producer to go towards higher usable shell thicknesses or increased residual shell thickness after scrap diameter in order to delay potential fatigue phenomena at the shell-core interface. One important parameter could not be evaluated in this study, it concerns the pollutions of the core material by alloying elements of the shell during production, which could affect to some extent the mechanical properties and
microstructure of the core. The macroscopic thermo-mechanical-metallurgical Finite Element model used to perform simulations, takes into account coupled effects. Input data parameters are identified by experimental tests such as compression tests at constant strain rate
and numerical procedures such as inverse method. After the model presentation, the material data set is commented. Whole experimental campaign could not be presented,
however interested readers are referred to [1] where more details on the material study of High Chromium Steel alloy can be found. The section of simulation results show the phase transformation histories and stress profiles of a typical roll of diameter 1.2 m and shell thickness of 0.08 m. An additional sensitivity analysis of the results to some material data such as
induced plasticity transformation coefficient and shift of the martensitic transformation start temperature parameters is reported. Finally, some conclusions analyze the interest and drawbacks of the described model and its results.Resiliency of a Community of Buildings to Fire Following Earthquake
http://hdl.handle.net/2268/183065
Title: Resiliency of a Community of Buildings to Fire Following Earthquake
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<br/>Author, co-author: Gernay, Thomas; Elhami Khorasani, Negar; Garlock, Maria
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<br/>Abstract: Cascading multi-hazard events, such as fires following an earthquake, can trigger progressive collapse of structures. In cascading earthquake and fire events, buildings that may have already experienced damage due to a primary earthquake hazard, should cope with a secondary extreme event. This work provides a methodology to evaluate the risk of fire ignitions after an earthquake and building responses in a community. The work has two components: In the first part, a model is developed for predicting the probability of ignition in a building due to an earthquake. This probabilistic model relies on the data from seven significant earthquakes that took place in the U.S. between 1983 and 2014. The main parameters influencing the probability of ignition are found to be the peak ground acceleration, the type of building material, and the main features of the environment in which the buildings are located (i.e. the total square footage and the population density). In the second part of this work, fragility curves are developed for performance of structures under fire, to quantify the probability of exceeding a damage state given a fire scenario. The probabilistic ignition model is implemented in Ergo/Maeviz, a GIS based risk assessment software platform developed at the Mid-America Earthquake Center at UIUC. Ergo/Maeviz provides the probability of ignition after an earthquake for each building in a region of study, and the overall risk for the community. The developed package in Ergo/Maeviz is validated against number of historical fire following earthquake events. For the future work, the developed fragility curves for buildings under fire will be implemented in Ergo/Maeviz to integrate the probability of ignition and possible damage states of the buildings. This research integrates multi-hazard analysis and risk management to plan mitigation and recovery strategies, and to obtain resilient communities.