The Experts below are selected from a list of 13005 Experts worldwide ranked by ideXlab platform
Fehmi Cirak - One of the best experts on this subject based on the ideXlab platform.
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Isogeometric Shape Optimisation of shell structures using multiresolution subdivision surfaces
Computer-Aided Design, 2018Co-Authors: Kosala Bandara, Fehmi CirakAbstract:Abstract We introduce the isogeometric Shape Optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull–Clark subdivision schemes are considered for geometry modelling and finite element analysis. A gradient-based Shape Optimisation technique is implemented to minimise compliance, i.e. to maximise stiffness. Different control meshes describing the same surface are used for geometry representation, Optimisation and finite element analysis. The finite element analysis is performed with subdivision basis functions corresponding to a sufficiently refined control mesh. During iterative Shape Optimisation the geometry is updated starting from the coarsest control mesh and proceeding to increasingly finer control meshes. This multiresolution approach provides a means for regularising the Optimisation problem and prevents the appearance of sub-optimal jagged geometries with fine-scale oscillations. The finest control mesh for Optimisation is chosen in accordance with the desired smallest feature size in the optimised geometry. The proposed approach is applied to three Optimisation examples, namely a catenary, a roof over a rectangular domain and a freeform architectural shell roof. The influence of the geometry description and the used subdivision scheme on the obtained optimised curved geometries is investigated in detail.
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Isogeometric Shape Optimisation of shell structures using multiresolution subdivision surfaces
Journal of Physics: Conference Series, 2016Co-Authors: Xiao Xiao, Kosala Bandara, Fehmi CirakAbstract:We introduce the isogeometric Shape Optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element analysis. A gradient-based Shape Optimisation technique is implemented to minimise compliance, i.e. to maximise stiffness. Different control meshes describing the same surface are used for geometry representation, Optimisation and finite element analysis. The finite element analysis is performed with subdivision basis functions corresponding to a sufficiently fine control mesh. During iterative Shape Optimisation the geometry is updated starting from the coarsest control mesh and proceeding to increasingly finer control meshes. The proposed approach is applied to three Optimisation examples, namely a catenary, a roof over a rectangular domain, and free-form architectural shell roof. The influence of the geometry description and the used subdivision scheme on the obtained optimised curved geometries are investigated in detail.
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Shape Optimisation with multiresolution subdivision surfaces and immersed finite elements
Computer Methods in Applied Mechanics and Engineering, 2016Co-Authors: Kosala Bandara, Thomas Rüberg, Fehmi CirakAbstract:Abstract We develop a new Optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of Optimisation. Similar to wavelets, multiresolution surfaces represent the domain boundary using a coarse control mesh and a sequence of detail vectors. Based on the multiresolution decomposition efficient and fast algorithms are available for reconstructing control meshes of varying fineness. During Shape Optimisation the vertex coordinates of control meshes are updated using the computed Shape gradient information. By virtue of the multiresolution editing semantics, updating the coarse control mesh vertex coordinates leads to large-scale geometry changes and, conversely, updating the fine control mesh coordinates leads to small-scale geometry changes. In our computations we start by optimising the coarsest control mesh and refine it each time the cost function reaches a minimum. This approach effectively prevents the appearance of non-physical boundary geometry oscillations and control mesh pathologies, like inverted elements. Independent of the fineness of the control mesh used for Optimisation, on the immersed finite element grid the domain boundary is always represented with a relatively fine control mesh of fixed resolution. With the immersed finite element method there is no need to maintain an analysis suitable domain mesh. In some of the presented two and three-dimensional elasticity examples the topology derivative is used for introducing new holes inside the domain. The merging or removing of holes is not considered.
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Multiresolution Shape Optimisation with Subdivision Surfaces
Lecture Notes in Computational Science and Engineering, 2015Co-Authors: Fehmi Cirak, Kosala BandaraAbstract:We review our recent work on multiresolution Shape Optimisation and present its application to elastic solids, electrostatic field equations and thin-shells. In the spirit of isogeometric analysis the geometry of the domain is described with subdivision surfaces and different resolutions of the same surface are used for Optimisation and analysis. The analysis is performed using a sufficiently fine control mesh with a fixed resolution. During Shape Optimisation the geometry is updated starting with the coarsest control mesh and then moving on to increasingly finer control meshes. The transfer of data between the geometry and analysis representations is accomplished with subdivision refinement and coarsening operators. Moreover, we discretise elastic solids with the immersed finite element method, electrostatic field equations with the boundary element method and thin-shells with the subdivision finite element technique. In all three discretisation techniques there is no need to generate and maintain an analysis-suitable volume discretisation.
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Boundary element based multiresolution Shape Optimisation in electrostatics
Journal of Computational Physics, 2015Co-Authors: Kosala Bandara, Fehmi Cirak, Olaf Steinbach, Jan ZapletalAbstract:We consider the Shape Optimisation of high-voltage devices subject to electrostatic field equations by combining fast boundary elements with multiresolution subdivision surfaces. The geometry of the domain is described with subdivision surfaces and different resolutions of the same geometry are used for Optimisation and analysis. The primal and adjoint problems are discretised with the boundary element method using a sufficiently fine control mesh. For Shape Optimisation the geometry is updated starting from the coarsest control mesh with increasingly finer control meshes. The multiresolution approach effectively prevents the appearance of non-physical geometry oscillations in the optimised Shapes. Moreover, there is no need for mesh regeneration or smoothing during the Optimisation due to the absence of a volume mesh. We present several numerical experiments and one industrial application to demonstrate the robustness and versatility of the developed approach.
Franz-joseph Barthold - One of the best experts on this subject based on the ideXlab platform.
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Two-scale Shape Optimisation based on numerical homogenisation techniques and variational sensitivity analysis
Computational Mechanics, 2021Co-Authors: Wojciech Kijanski, Franz-joseph BartholdAbstract:This contribution presents a theoretical and computational framework for two-scale Shape Optimisation of nonlinear elastic structures. Particularly, minimum compliance Optimisation problems with composite (matrix-inclusion) microstructures subjected to static loads and volume-type design constraints are focused. A homogenisation-based FE $$^2$$ 2 scheme is extended by an enhanced formulation of variational (Shape) sensitivity analysis based on Noll ’s intrinsic, frame-free formulation of continuum mechanics. The obtained overall two-scale sensitivity information couples Shape variations across micro- and macroscopic scales. A numerical example demonstrates the capabilities of the proposed variational sensitivity analysis and the (Shape) Optimisation framework. The investigations involve a mesh morphing scheme for the design parametrisation at both macro- and microscopic scales.
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Shape Optimisation analysing the inner structure of sensitivity matrices
PAMM, 2011Co-Authors: Nikolai Gerzen, Franz-joseph BartholdAbstract:This contribution deals with sensitivity analysis in nodal based Shape Optimisation. Sensitivity analysis is one of the most important parts of a structural Optimisation algorithm. The efficiency of the algorithm mainly depends on the obtained sensitivity information. The pseudo load and sensitivity matrices which appear in sensitivity analysis are commonly used to derive and to calculate the gradients and the Hessian matrices of objective functions and of constraints. The aim of this contribution is to show that these matrices contain additional useful information which is not used in structural Optimisation until now. We demonstrate the opportunities and capabilities of the new information which are obtained by singular value decomposition (SVD) of the pseudo load and sensitivity matrices and by eigenvalue decomposition of the Hessian matrix. Furthermore, we avoid jagged boundaries in Shape Optimisation by applying a density filtering technique well-known in topology Optimisation. Numerical examples illustrate the advocated theoretical concept. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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The inner structure of sensitivities in nodal based Shape Optimisation
Computational Mechanics, 2011Co-Authors: Nikolai Gerzen, Daniel Materna, Franz-joseph BartholdAbstract:The pseudo load matrix and the sensitivity matrix dominate design sensitivity analysis of Shape Optimisation problems. They describe how a structure reacts on an imposed design modification. We analyse these matrices for the model problem of nodal based Shape Optimisation by a singular value decomposition and show that they contain additional valuable information which is not yet used either in theory or computation of Shape Optimisation. The inner structure of the sensitivities is capable to formulate reduced quadratic sub-problems within the sequential quadratic programming approach. We also tackle the problem of indefinite Hessian matrices in nodal based Shape Optimisation. Furthermore, we avoid jagged boundaries and obtain mesh-independent optimised structures applying density filtering technique to Shape Optimisation. Overall, we emphasise an enhanced analysis of sensitivities and point to unused substantial capabilities.
Kosala Bandara - One of the best experts on this subject based on the ideXlab platform.
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Isogeometric Shape Optimisation of shell structures using multiresolution subdivision surfaces
Computer-Aided Design, 2018Co-Authors: Kosala Bandara, Fehmi CirakAbstract:Abstract We introduce the isogeometric Shape Optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull–Clark subdivision schemes are considered for geometry modelling and finite element analysis. A gradient-based Shape Optimisation technique is implemented to minimise compliance, i.e. to maximise stiffness. Different control meshes describing the same surface are used for geometry representation, Optimisation and finite element analysis. The finite element analysis is performed with subdivision basis functions corresponding to a sufficiently refined control mesh. During iterative Shape Optimisation the geometry is updated starting from the coarsest control mesh and proceeding to increasingly finer control meshes. This multiresolution approach provides a means for regularising the Optimisation problem and prevents the appearance of sub-optimal jagged geometries with fine-scale oscillations. The finest control mesh for Optimisation is chosen in accordance with the desired smallest feature size in the optimised geometry. The proposed approach is applied to three Optimisation examples, namely a catenary, a roof over a rectangular domain and a freeform architectural shell roof. The influence of the geometry description and the used subdivision scheme on the obtained optimised curved geometries is investigated in detail.
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Isogeometric Shape Optimisation of shell structures using multiresolution subdivision surfaces
Journal of Physics: Conference Series, 2016Co-Authors: Xiao Xiao, Kosala Bandara, Fehmi CirakAbstract:We introduce the isogeometric Shape Optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element analysis. A gradient-based Shape Optimisation technique is implemented to minimise compliance, i.e. to maximise stiffness. Different control meshes describing the same surface are used for geometry representation, Optimisation and finite element analysis. The finite element analysis is performed with subdivision basis functions corresponding to a sufficiently fine control mesh. During iterative Shape Optimisation the geometry is updated starting from the coarsest control mesh and proceeding to increasingly finer control meshes. The proposed approach is applied to three Optimisation examples, namely a catenary, a roof over a rectangular domain, and free-form architectural shell roof. The influence of the geometry description and the used subdivision scheme on the obtained optimised curved geometries are investigated in detail.
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Shape Optimisation with multiresolution subdivision surfaces and immersed finite elements
Computer Methods in Applied Mechanics and Engineering, 2016Co-Authors: Kosala Bandara, Thomas Rüberg, Fehmi CirakAbstract:Abstract We develop a new Optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of Optimisation. Similar to wavelets, multiresolution surfaces represent the domain boundary using a coarse control mesh and a sequence of detail vectors. Based on the multiresolution decomposition efficient and fast algorithms are available for reconstructing control meshes of varying fineness. During Shape Optimisation the vertex coordinates of control meshes are updated using the computed Shape gradient information. By virtue of the multiresolution editing semantics, updating the coarse control mesh vertex coordinates leads to large-scale geometry changes and, conversely, updating the fine control mesh coordinates leads to small-scale geometry changes. In our computations we start by optimising the coarsest control mesh and refine it each time the cost function reaches a minimum. This approach effectively prevents the appearance of non-physical boundary geometry oscillations and control mesh pathologies, like inverted elements. Independent of the fineness of the control mesh used for Optimisation, on the immersed finite element grid the domain boundary is always represented with a relatively fine control mesh of fixed resolution. With the immersed finite element method there is no need to maintain an analysis suitable domain mesh. In some of the presented two and three-dimensional elasticity examples the topology derivative is used for introducing new holes inside the domain. The merging or removing of holes is not considered.
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Multiresolution Shape Optimisation with Subdivision Surfaces
Lecture Notes in Computational Science and Engineering, 2015Co-Authors: Fehmi Cirak, Kosala BandaraAbstract:We review our recent work on multiresolution Shape Optimisation and present its application to elastic solids, electrostatic field equations and thin-shells. In the spirit of isogeometric analysis the geometry of the domain is described with subdivision surfaces and different resolutions of the same surface are used for Optimisation and analysis. The analysis is performed using a sufficiently fine control mesh with a fixed resolution. During Shape Optimisation the geometry is updated starting with the coarsest control mesh and then moving on to increasingly finer control meshes. The transfer of data between the geometry and analysis representations is accomplished with subdivision refinement and coarsening operators. Moreover, we discretise elastic solids with the immersed finite element method, electrostatic field equations with the boundary element method and thin-shells with the subdivision finite element technique. In all three discretisation techniques there is no need to generate and maintain an analysis-suitable volume discretisation.
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Boundary element based multiresolution Shape Optimisation in electrostatics
Journal of Computational Physics, 2015Co-Authors: Kosala Bandara, Fehmi Cirak, Olaf Steinbach, Jan ZapletalAbstract:We consider the Shape Optimisation of high-voltage devices subject to electrostatic field equations by combining fast boundary elements with multiresolution subdivision surfaces. The geometry of the domain is described with subdivision surfaces and different resolutions of the same geometry are used for Optimisation and analysis. The primal and adjoint problems are discretised with the boundary element method using a sufficiently fine control mesh. For Shape Optimisation the geometry is updated starting from the coarsest control mesh with increasingly finer control meshes. The multiresolution approach effectively prevents the appearance of non-physical geometry oscillations in the optimised Shapes. Moreover, there is no need for mesh regeneration or smoothing during the Optimisation due to the absence of a volume mesh. We present several numerical experiments and one industrial application to demonstrate the robustness and versatility of the developed approach.
Eckhard Finke - One of the best experts on this subject based on the ideXlab platform.
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Shape Optimisation by design of experiments and finite element methods—an application of steel wheels
Structural and Multidisciplinary Optimization, 2008Co-Authors: Christina Schäfer, Eckhard FinkeAbstract:The requirements made on industry, and particularly on development departments, are increasing constantly due to demands to reduce costs and development times and the introduction of new quality guidelines (Toutenburg and Gössl, Versuchsplanung in der industrie; moderne methoden und softwarelösungen. Proceedings des workshops versuchsplanung in der industrie der boehringer mannheim GmbH und SAS-Institute, Tutzing 30./31.10.1995. Prentice Hall Verlag, München, 1996 ). In particular, several loops are usually required within the development process during the development of new parts to obtain an optimal part Shape. This process is extensively influenced by the experience and know-how of the developer or design engineer. A method that enables a specific and structured approach to part Shape Optimisation is presented in this paper. Design of experiments and the finite element method are interlinked in this method.
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Shape Optimisation by design of experiments and finite element methods an application of steel wheels
Structural and Multidisciplinary Optimization, 2008Co-Authors: Christina Schäfer, Eckhard FinkeAbstract:The requirements made on industry, and particularly on development departments, are increasing constantly due to demands to reduce costs and development times and the introduction of new quality guidelines (Toutenburg and Gossl, Versuchsplanung in der industrie; moderne methoden und softwarelosungen. Proceedings des workshops versuchsplanung in der industrie der boehringer mannheim GmbH und SAS-Institute, Tutzing 30./31.10.1995. Prentice Hall Verlag, Munchen, 1996). In particular, several loops are usually required within the development process during the development of new parts to obtain an optimal part Shape. This process is extensively influenced by the experience and know-how of the developer or design engineer. A method that enables a specific and structured approach to part Shape Optimisation is presented in this paper. Design of experiments and the finite element method are interlinked in this method.
Lip H. Teh - One of the best experts on this subject based on the ideXlab platform.
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Shape Optimisation of cold-formed steel columns with manufacturing constraints using the Hough transform
Thin-Walled Structures, 2016Co-Authors: Bin Wang, Benoit P. Gilbert, Hong Guan, Adrien M. Molinier, Lip H. TehAbstract:This paper introduces manufacturing constraints into a recently developed evolutionary algorithm for Shape Optimisation of CFS profiles. The algorithm is referred to as “self-Shape Optimisation” and uses Genetic Algorithm (GA) together with the Augmented Lagrangian (AL) method to avoid ill-conditioned problems. Simple manufacturing rules derived from the limitations of current cold-forming processes, i.e. a limited ability to form continuously curved surfaces without discrete bends, are described in the paper and incorporated into the algorithm. The Hough transform is used to detect straight lines and transform arbitrarily drawn cross-sections into manufacturable ones. Firstly, the algorithm is verified against a known Optimisation problem and found to accurately converge to a manufacturable optimum solution. Secondly, the algorithm is applied to singly-symmetric CFS columns each of which is subject to an axial compressive load of 75kN and has a uniform wall thickness of 1.2 mm. The strength of the columns is evaluated by the Direct Strength Method (DSM) and all buckling modes are considered. Various column lengths (from 500 mm to 3000 mm) and numbers of roll-forming bends were investigated. The optimised cross-sections are presented and discussed.
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Unconstrained Shape Optimisation of singly-symmetric and open cold-formed steel beams and beam-columns
Thin-Walled Structures, 2016Co-Authors: Bin Wang, Benoit P. Gilbert, Hong Guan, Guillaume L. Bosco, Lip H. TehAbstract:This study aims to optimise the cross-sectional Shape of singly-symmetric, open-section and simply-supported cold-formed steel (CFS) beams and beam-columns. No manufacturing or assembly constraints are considered. The previously developed augmented Lagrangian Genetic Algorithm (GA), referred to as the “self-Shape” Optimisation algorithm, is used herein. Fully restrained and unrestrained beams against lateral deflection and twist, as well as unrestrained beam-columns are optimised. Various combinations of axial compressive load and bending moment are analysed for the beam-columns. The Direct Strength Method (DSM) is used to evaluate the nominal member compressive and bending capacities. The accuracy of the automated rules, developed in the literature to determine the elastic local and distortional axial buckling stresses from Finite Strip signature curves, is verified herein to estimate the elastic bending buckling stresses. The optimised cross-sectional Shapes are presented for all cases and the evolution of the unrestrained Shapes from pure axial compression to pure bending is discussed.
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Shape Optimisation of manufacturable and usable cold-formed steel singly-symmetric and open columns
Thin-Walled Structures, 2016Co-Authors: Bin Wang, Benoit P. Gilbert, Hong Guan, Lip H. TehAbstract:This paper aims at incorporating manufacturing and assembly features into a Shape Optimisation algorithm for cold-formed steel (CFS) profiles. Genetic algorithm (GA) is used as the search algorithm and is combined with the augmented Lagrangian constraint-handling method to avoid ill-conditioning. Manufacturable cross-sections are arbitrarily drawn in the initial generation and subsequently treated as an integral part of the GA. The assembly features considered in the study reflect the ones commonly encountered in the construction industry. They include fastening elements (horizontal flange and vertical web) and allowances for utilities, and are treated as constraints. The algorithm is applied to simply-supported singly-symmetric, free-to-warp open section columns with various numbers of manufacturing bends. Three assembly cases for half sections are investigated: (a) a horizontal flange, (b) a horizontal flange and a vertical web, and (c) a horizontal flange and a vertical web with a utility clearance. A two-step Optimisation process is used to optimise the columns: (i) the optimum positions of the fastening elements (horizontal flange and vertical web) are determined first and (ii) the cross-sectional Shapes are then optimised. The optimised columns are discussed and compared to the unconstrained optimised columns and the conventional lipped Cee-sections. The results demonstrate the robustness and efficiency of the algorithm.
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Likelihood of buckling mode interaction in Shape Optimisation of manufacturable cold-formed steel columns
2015Co-Authors: Bin Wang, Benoit P. Gilbert, Hong Guan, Lip H. TehAbstract:This paper investigates the likelihood of buckling mode interaction in Shape Optimisation of manufacturable cold-formed steel columns. A literature review is carried out to examine local, distortional and global buckling mode interactions. Optimised columns available in the literature and the research outcomes previously carried out by the authors are discussed in some detail. The average elastic buckling stresses are reported herein and the need for incorporating the buckling mode interactions into Shape Optimisation algorithms is quantified.
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Shape Optimisation of cold-formed steel profiles with manufacturing constraints – Part II: Applications
2014Co-Authors: Bin Wang, Benoit P. Gilbert, Hong Guan, Adrien M. Molinier, Lip H. TehAbstract:This paper presents a Genetic Algorithm Optimisation method with manufacturing constraints for Shape Optimisation of cold-formed steel (CFS) profiles. Previous studies on unconstrained Shape Optimisation of CFS crosssections, where the sole aim was to optimise the weight-to-capacity ratio of the profiles, yielded cross-sections that cannot be manufactured. Current coldforming processes, such as roll-forming and brake-pressing, have limited ability to form continuously curved surfaces without discrete bends. This paper defines simple manufacturing rules and introduces them into the evolutionary algorithm. Augmented Lagrangian constraint-handling technique, with equality and inequality constrained violations, is used to avoid ill-conditioned problems. The ability and accuracy of the algorithm to handle the defined manufacturing constraints are verified by implementing it to optimise the section capacity of bisymmetric closed thin-walled profiles, for which an analytical solution is known.