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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 19 Apr 2024 14:51:16 GMT2024-04-19T14:51:16ZProper Generalized Decomposition for Parametric Study and Material Distribution Design of Multi-Directional Functionally Graded Plates Based on 3D Elasticity Solution
http://hdl.handle.net/10985/23283
Proper Generalized Decomposition for Parametric Study and Material Distribution Design of Multi-Directional Functionally Graded Plates Based on 3D Elasticity Solution
KAZEMZADEH-PARSI, Mohammad-Javad; CHINESTA, Francisco; AMMAR, Amine
The use of mesh-based numerical methods for a 3D elasticity solution of thick plates involves high computational costs. This particularly limits parametric studies and material distribution design problems because they need a large number of independent simulations to evaluate the effects of material distribution and optimization. In this context, in the current work, the Proper Generalized Decomposition (PGD) technique is adopted to overcome this difficulty and solve the 3D elasticity problems in a high-dimensional parametric space. PGD is an a priori model order reduction technique that reduces the solution of 3D partial differential equations into a set of 1D ordinary differential equations, which can be solved easily. Moreover, PGD makes it possible to perform parametric solutions in a unified and efficient manner. In the present work, some examples of a parametric elasticity solution and material distribution design of multi-directional FGM composite thick plates are presented after some validation case studies to show the applicability of PGD in such problems.
Thu, 04 Nov 2021 00:00:00 GMThttp://hdl.handle.net/10985/232832021-11-04T00:00:00ZKAZEMZADEH-PARSI, Mohammad-JavadCHINESTA, FranciscoAMMAR, AmineThe use of mesh-based numerical methods for a 3D elasticity solution of thick plates involves high computational costs. This particularly limits parametric studies and material distribution design problems because they need a large number of independent simulations to evaluate the effects of material distribution and optimization. In this context, in the current work, the Proper Generalized Decomposition (PGD) technique is adopted to overcome this difficulty and solve the 3D elasticity problems in a high-dimensional parametric space. PGD is an a priori model order reduction technique that reduces the solution of 3D partial differential equations into a set of 1D ordinary differential equations, which can be solved easily. Moreover, PGD makes it possible to perform parametric solutions in a unified and efficient manner. In the present work, some examples of a parametric elasticity solution and material distribution design of multi-directional FGM composite thick plates are presented after some validation case studies to show the applicability of PGD in such problems.Domain decomposition involving subdomain separable space representations for solving parametric problems in complex geometries
http://hdl.handle.net/10985/22202
Domain decomposition involving subdomain separable space representations for solving parametric problems in complex geometries
KAZEMZADEH-PARSI, Mohammad-Javad; AMMAR, Amine; CHINESTA, Francisco
A domain decomposition technique combined with an enhanced geometry mapping based on the use of NURBS is considered for solving parametrized models in complex geometries (non simply connected) within the so-called proper generalized decomposition (PGD) framework, enabling the expression of the solution in each subdomain in a fully separated form, involving both the space and the model parameters. NURBS allow a compact and powerful domain mapping into a fully separated reference geometry, while the PGD allows recovering an affine structure of the problem in the reference domain, facilitating the use of the standard PGD solver for computing the parametric solution in each subdomain first, and then by enforcing the interface transmission conditions, in the whole domain.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10985/222022022-01-01T00:00:00ZKAZEMZADEH-PARSI, Mohammad-JavadAMMAR, AmineCHINESTA, FranciscoA domain decomposition technique combined with an enhanced geometry mapping based on the use of NURBS is considered for solving parametrized models in complex geometries (non simply connected) within the so-called proper generalized decomposition (PGD) framework, enabling the expression of the solution in each subdomain in a fully separated form, involving both the space and the model parameters. NURBS allow a compact and powerful domain mapping into a fully separated reference geometry, while the PGD allows recovering an affine structure of the problem in the reference domain, facilitating the use of the standard PGD solver for computing the parametric solution in each subdomain first, and then by enforcing the interface transmission conditions, in the whole domain.Parametric Analysis of Thick FGM Plates Based on 3D Thermo-Elasticity Theory: A Proper Generalized Decomposition Approach
http://hdl.handle.net/10985/24728
Parametric Analysis of Thick FGM Plates Based on 3D Thermo-Elasticity Theory: A Proper Generalized Decomposition Approach
KAZEMZADEH-PARSI, Mohammad-Javad; AMMAR, Amine; CHINESTA SORIA, Francisco
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Parametric Analysis of Thick FGM Plates Based on 3D Thermo-Elasticity Theory: A Proper Generalized Decomposition Approach
by Mohammad-Javad Kazemzadeh-Parsi
1,* [ORCID] , Amine Ammar
1 [ORCID] and Francisco Chinesta
2
1
LAMPA & ESI Group Chair, Arts et Metiers Institute of Technology, 49035 Angers, France
2
PIMM Lab & ESI Group Chair, Arts et Metiers Institute of Technology, 75013 Paris, France
*
Author to whom correspondence should be addressed.
Materials 2023, 16(4), 1753; https://doi.org/10.3390/ma16041753
Submission received: 19 December 2022 / Revised: 10 February 2023 / Accepted: 17 February 2023 / Published: 20 February 2023
(This article belongs to the Topic Artificial Intelligence and Computational Methods: Modeling, Simulations and Optimization of Complex Systems)
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In the present work, the general and well-known model reduction technique, PGD (Proper Generalized Decomposition), is used for parametric analysis of thermo-elasticity of FGMs (Functionally Graded Materials). The FGMs have important applications in space technologies, especially when a part undergoes an extreme thermal environment. In the present work, material gradation is considered in one, two and three directions, and 3D heat transfer and theory of elasticity equations are solved to have an accurate temperature field and be able to consider all shear deformations. A parametric analysis of FGM materials is especially useful in material design and optimization. In the PGD technique, the field variables are separated to a set of univariate functions, and the high-dimensional governing equations reduce to a set of one-dimensional problems. Due to the curse of dimensionality, solving a high-dimensional parametric problem is considerably more computationally intensive than solving a set of one-dimensional problems. Therefore, the PGD makes it possible to handle high-dimensional problems efficiently. In the present work, some sample examples in 4D and 5D computational spaces are solved, and the results are presented.
Sun, 01 Jan 2023 00:00:00 GMThttp://hdl.handle.net/10985/247282023-01-01T00:00:00ZKAZEMZADEH-PARSI, Mohammad-JavadAMMAR, AmineCHINESTA SORIA, Franciscofirst_page
settings
Order Article Reprints
Open AccessArticle
Parametric Analysis of Thick FGM Plates Based on 3D Thermo-Elasticity Theory: A Proper Generalized Decomposition Approach
by Mohammad-Javad Kazemzadeh-Parsi
1,* [ORCID] , Amine Ammar
1 [ORCID] and Francisco Chinesta
2
1
LAMPA & ESI Group Chair, Arts et Metiers Institute of Technology, 49035 Angers, France
2
PIMM Lab & ESI Group Chair, Arts et Metiers Institute of Technology, 75013 Paris, France
*
Author to whom correspondence should be addressed.
Materials 2023, 16(4), 1753; https://doi.org/10.3390/ma16041753
Submission received: 19 December 2022 / Revised: 10 February 2023 / Accepted: 17 February 2023 / Published: 20 February 2023
(This article belongs to the Topic Artificial Intelligence and Computational Methods: Modeling, Simulations and Optimization of Complex Systems)
Download
keyboard_arrow_down
Browse Figures
Versions Notes
Abstract
In the present work, the general and well-known model reduction technique, PGD (Proper Generalized Decomposition), is used for parametric analysis of thermo-elasticity of FGMs (Functionally Graded Materials). The FGMs have important applications in space technologies, especially when a part undergoes an extreme thermal environment. In the present work, material gradation is considered in one, two and three directions, and 3D heat transfer and theory of elasticity equations are solved to have an accurate temperature field and be able to consider all shear deformations. A parametric analysis of FGM materials is especially useful in material design and optimization. In the PGD technique, the field variables are separated to a set of univariate functions, and the high-dimensional governing equations reduce to a set of one-dimensional problems. Due to the curse of dimensionality, solving a high-dimensional parametric problem is considerably more computationally intensive than solving a set of one-dimensional problems. Therefore, the PGD makes it possible to handle high-dimensional problems efficiently. In the present work, some sample examples in 4D and 5D computational spaces are solved, and the results are presented.Describing and Modeling Rough Composites Surfaces by Using Topological Data Analysis and Fractional Brownian Motion
http://hdl.handle.net/10985/24797
Describing and Modeling Rough Composites Surfaces by Using Topological Data Analysis and Fractional Brownian Motion
RUNACHER, Antoine; KAZEMZADEH-PARSI, Mohammad-Javad; DI LORENZO, Daniele; CHAMPANEY, Victor; HASCOET, Nicolas; AMMAR, Amine; CHINESTA SORIA, Francisco
Many composite manufacturing processes employ the consolidation of pre-impregnated preforms. However, in order to obtain adequate performance of the formed part, intimate contact and molecular diffusion across the different composites’ preform layers must be ensured. The latter takes place as soon as the intimate contact occurs and the temperature remains high enough during the molecular reptation characteristic time. The former, in turn, depends on the applied compression force, the temperature and the composite rheology, which, during the processing, induce the flow of asperities, promoting the intimate contact. Thus, the initial roughness and its evolution during the process, become critical factors in the composite consolidation. Processing optimization and control are needed for an adequate model, enabling it to infer the consolidation degree from the material and process features. The parameters associated with the process are easily identifiable and measurable (e.g., temperature, compression force, process time, ⋯). The ones concerning the materials are also accessible; however, describing the surface roughness remains an issue. Usual statistical descriptors are too poor and, moreover, they are too far from the involved physics. The present paper focuses on the use of advanced descriptors out-performing usual statistical descriptors, in particular those based on the use of homology persistence (at the heart of the so-called topological data analysis—TDA), and their connection with fractional Brownian surfaces. The latter constitutes a performance surface generator able to represent the surface evolution all along the consolidation process, as the present paper emphasizes.
Sun, 01 Jan 2023 00:00:00 GMThttp://hdl.handle.net/10985/247972023-01-01T00:00:00ZRUNACHER, AntoineKAZEMZADEH-PARSI, Mohammad-JavadDI LORENZO, DanieleCHAMPANEY, VictorHASCOET, NicolasAMMAR, AmineCHINESTA SORIA, FranciscoMany composite manufacturing processes employ the consolidation of pre-impregnated preforms. However, in order to obtain adequate performance of the formed part, intimate contact and molecular diffusion across the different composites’ preform layers must be ensured. The latter takes place as soon as the intimate contact occurs and the temperature remains high enough during the molecular reptation characteristic time. The former, in turn, depends on the applied compression force, the temperature and the composite rheology, which, during the processing, induce the flow of asperities, promoting the intimate contact. Thus, the initial roughness and its evolution during the process, become critical factors in the composite consolidation. Processing optimization and control are needed for an adequate model, enabling it to infer the consolidation degree from the material and process features. The parameters associated with the process are easily identifiable and measurable (e.g., temperature, compression force, process time, ⋯). The ones concerning the materials are also accessible; however, describing the surface roughness remains an issue. Usual statistical descriptors are too poor and, moreover, they are too far from the involved physics. The present paper focuses on the use of advanced descriptors out-performing usual statistical descriptors, in particular those based on the use of homology persistence (at the heart of the so-called topological data analysis—TDA), and their connection with fractional Brownian surfaces. The latter constitutes a performance surface generator able to represent the surface evolution all along the consolidation process, as the present paper emphasizes.