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You searched for subject:(Ritz Vectors). Showing records 1 – 3 of 3 total matches.

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Delft University of Technology

1. Van der Linde, T.M. (author). Fast topology optimization for transient mechanical problems.

Degree: 2016, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:2aa17c56-66a2-41c8-95fc-a1af50dc52dd 

Topology optimization is increasingly used as a design tool in engineering. Within structural mechanics, most applications focus on statics. An extension to time-domain (transient) dynamics will have many useful applications, but this is currently hindered by high computational costs. The goal of this research is to reduce these costs by applying model order reduction. In model order reduction, the full coordinates of a system are approximated by a much smaller number of reduced coordinates and associated basis vectors. A few options for these vectors will be discussed. It is shown that using load-based methods results in high accuracy, especially the Ritz vector method. In the total optimization this leads to significant reduction of both CPU-time and memory requirements.

Engineering Mechanics

Precision and Microsystems Engineering

Mechanical, Maritime and Materials Engineering

Advisors/Committee Members: Langelaar, M. (mentor).

Subjects/Keywords: topology optimization; time-domain dynamics; transient dynamics; model order reduction; Ritz vectors

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Van der Linde, T. M. (. (2016). Fast topology optimization for transient mechanical problems. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:2aa17c56-66a2-41c8-95fc-a1af50dc52dd

Chicago Manual of Style (16th Edition):

Van der Linde, T M (author). “Fast topology optimization for transient mechanical problems.” 2016. Masters Thesis, Delft University of Technology. Accessed January 18, 2021. http://resolver.tudelft.nl/uuid:2aa17c56-66a2-41c8-95fc-a1af50dc52dd.

MLA Handbook (7th Edition):

Van der Linde, T M (author). “Fast topology optimization for transient mechanical problems.” 2016. Web. 18 Jan 2021.

Vancouver:

Van der Linde TM(. Fast topology optimization for transient mechanical problems. [Internet] [Masters thesis]. Delft University of Technology; 2016. [cited 2021 Jan 18]. Available from: http://resolver.tudelft.nl/uuid:2aa17c56-66a2-41c8-95fc-a1af50dc52dd.

Council of Science Editors:

Van der Linde TM(. Fast topology optimization for transient mechanical problems. [Masters Thesis]. Delft University of Technology; 2016. Available from: http://resolver.tudelft.nl/uuid:2aa17c56-66a2-41c8-95fc-a1af50dc52dd


Delft University of Technology

2. Holtzer, Bart (author). Topology Optimization of Geometrically Nonlinear Structures.

Degree: 2017, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:95ae533b-4b37-4d4a-92f5-029735a09265 

So far, structural topology optimization has been mainly focused on linear problems. Much less attention has been paid to geometrically nonlinear problems, although it has a lot of interesting applications. The objective of this work is to implement a method to solve topology optimization problems under finite displacements and rotations. The main focus is on designing stiff structures, but also an outlook is presented on the design of structures that follow a prescribed equilibrium path. The Newton-Raphson incremental-iterative procedure is implemented to solve nonlinear problems. Arc-length control is used to be able to overcome limit points and to obtain faster convergence. It is shown by means of numerical experiments that this method leads to correct results. Since nonlinear analysis, especially in combination with topology optimization, is computationally expensive, an attempt is made to develop a new reduction method. This method uses load dependent Ritz vectors as a reduced basis and was originally used in linear dynamic problems. However, it is demonstrated that this method will in general not lead to accurate results in nonlinear static problems. This is due to the fact that deformation modes that are not excited by the external force, cannot be described by the basis. The topology optimization process is implemented without reduction method. An adjoint formulation is derived to obtain sensitivities in a computationally efficient way. By means of several examples of end-compliance minimization, it is demonstrated that in most cases, especially for shell structures, this method leads to better performing designs than topology optimization based on linear analysis. Advisors/Committee Members: van Keulen, Fred (mentor), Delft University of Technology (degree granting institution).

Subjects/Keywords: topology optimization; geometrically nonlinear structures; Ritz vectors; nonlinear mechanics; arc-length control; prescribed equilibrium paths; shells; Reduced order model

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Holtzer, B. (. (2017). Topology Optimization of Geometrically Nonlinear Structures. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:95ae533b-4b37-4d4a-92f5-029735a09265

Chicago Manual of Style (16th Edition):

Holtzer, Bart (author). “Topology Optimization of Geometrically Nonlinear Structures.” 2017. Masters Thesis, Delft University of Technology. Accessed January 18, 2021. http://resolver.tudelft.nl/uuid:95ae533b-4b37-4d4a-92f5-029735a09265.

MLA Handbook (7th Edition):

Holtzer, Bart (author). “Topology Optimization of Geometrically Nonlinear Structures.” 2017. Web. 18 Jan 2021.

Vancouver:

Holtzer B(. Topology Optimization of Geometrically Nonlinear Structures. [Internet] [Masters thesis]. Delft University of Technology; 2017. [cited 2021 Jan 18]. Available from: http://resolver.tudelft.nl/uuid:95ae533b-4b37-4d4a-92f5-029735a09265.

Council of Science Editors:

Holtzer B(. Topology Optimization of Geometrically Nonlinear Structures. [Masters Thesis]. Delft University of Technology; 2017. Available from: http://resolver.tudelft.nl/uuid:95ae533b-4b37-4d4a-92f5-029735a09265


University of Houston

3. Khoury, George Charles. Analyzing the Effects of Force Variations on Expanded Residual Damage Detection using Load Dependent Ritz Vectors.

Degree: MS, Mechanical Engineering, 2014, University of Houston

URL: http://hdl.handle.net/10657/1388 

Many non-destructive damage detection problems are presented with the challenge where limited sensor sets allow the measurement of fewer degrees of freedom than the analytical model. This study utilized damage residual expansion methods to determine the overall structural damage locations with reduced sensor sets. The new methods presented were the Modified Method of Expanded Dynamic Residuals and the Dot Product Damage Residual Expansion Method. Ritz vectors were also used with various sensor placement techniques to modify the sensor sets and focus the damage detection capabilities towards elements of interest. The results showed that the modified damage residual expansion methods were able to locate the damaged elements, while also simplifying the selection process, by employing the dot product method and the elemental disassembly. Additionally, the sensor set variations effectively focused the damage detection results towards elements of interest by modifying the Ritz vector loadings. Advisors/Committee Members: Franchek, Matthew A. (advisor), Grigoriadis, Karolos M. (committee member), Provence, Robert S. (committee member), Masson, Philippe J. (committee member).

Subjects/Keywords: Damage Detection; Minimum Rank Perturbation Theory; Damage Residuals; Method of Expanded Dynamic Residuals; Modified Method of Expanded Dynamic Residuals; Dot Product Damage Residual Expansion Method; Ritz Vectors

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Khoury, G. C. (2014). Analyzing the Effects of Force Variations on Expanded Residual Damage Detection using Load Dependent Ritz Vectors. (Masters Thesis). University of Houston. Retrieved from http://hdl.handle.net/10657/1388

Chicago Manual of Style (16th Edition):

Khoury, George Charles. “Analyzing the Effects of Force Variations on Expanded Residual Damage Detection using Load Dependent Ritz Vectors.” 2014. Masters Thesis, University of Houston. Accessed January 18, 2021. http://hdl.handle.net/10657/1388.

MLA Handbook (7th Edition):

Khoury, George Charles. “Analyzing the Effects of Force Variations on Expanded Residual Damage Detection using Load Dependent Ritz Vectors.” 2014. Web. 18 Jan 2021.

Vancouver:

Khoury GC. Analyzing the Effects of Force Variations on Expanded Residual Damage Detection using Load Dependent Ritz Vectors. [Internet] [Masters thesis]. University of Houston; 2014. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/10657/1388.

Council of Science Editors:

Khoury GC. Analyzing the Effects of Force Variations on Expanded Residual Damage Detection using Load Dependent Ritz Vectors. [Masters Thesis]. University of Houston; 2014. Available from: http://hdl.handle.net/10657/1388

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