FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W48934524> ?p ?o ?g. }

• W48934524 abstract "Topology optimization is a tool for finding a domain in which material is placed that optimizes a certain objective function subject to constraints. This thesis considers topology optimization for structural mechanics problems, where the underlying PDE is derived from linear elasticity. There are two main approaches for solving topology optimization: Solid Isotropic Material with Penalisation (SIMP) and Evolutionary Structural Optimization (ESO). SIMP is a continuous relaxation of the problem solved using a mathematical programming technique and so inherits the convergence properties of the optimization method. By contrast, ESO is based on engineering heuristics and has no proof of optimality. This thesis considers the formulation of the SIMP method as a mathematical optimization problem. Including the linear elasticity state equations is considered and found to be substantially less reliable and less efficient than excluding them from the formulation and solving the state equations separately. The convergence of the SIMP method under a regularising filter is investigated and shown to impede convergence. A robust criterion to stop filtering is proposed and demonstrated to work well in high-resolution problems (O(10^6)). The ESO method is investigated to fully explain its non-monotonic convergence behaviour. Through a series of analytic examples, the steps taken by the ESO algorithm are shown to differ arbitrarily from a linear approximation. It is this difference between the linear approximation and the actual value taken which causes ESO to occasionally take non-descent steps. A mesh refinement technique has been introduced with the sole intention of reducing the ESO step size and thereby ensuring descent of the algorithm. This is shown to work on numerous examples. Extending the classical topology optimization problem to included a global buckling constraint is considered. This poses multiple computational challenges, including the introduction of numerically driven spurious localised buckling modes and ill-defined gradients in the case of non-simple eigenvalues. To counter such issues that arise in a continuous relaxation approach, a method for solving the problem that enforces the binary constraints is proposed. The method is designed specifically to reduce the number of derivative calculations made, which is by far the most computationally expensive step in optimization involving buckling. This method is tested on multiple problems and shown to work on problems of size O(10^5)." @default.
• W48934524 created "2016-06-24" @default.
• W48934524 creator A5030856303 @default.
• W48934524 date "2013-05-01" @default.
• W48934524 modified "2023-09-25" @default.
• W48934524 title "Topology Optimization of Linear Elastic Structures" @default.
• W48934524 cites W117273804 @default.
• W48934524 cites W119682313 @default.
• W48934524 cites W147998453 @default.
• W48934524 cites W1520007244 @default.
• W48934524 cites W1536103813 @default.
• W48934524 cites W1547784515 @default.
• W48934524 cites W1551542124 @default.
• W48934524 cites W1566137732 @default.
• W48934524 cites W1569904303 @default.
• W48934524 cites W1575923498 @default.
• W48934524 cites W1677824830 @default.
• W48934524 cites W169036920 @default.
• W48934524 cites W1964471043 @default.
• W48934524 cites W1965748532 @default.
• W48934524 cites W1970101292 @default.
• W48934524 cites W1970321781 @default.
• W48934524 cites W1971811031 @default.
• W48934524 cites W1975067325 @default.
• W48934524 cites W1979756260 @default.
• W48934524 cites W1980907613 @default.
• W48934524 cites W1982647060 @default.
• W48934524 cites W1984363919 @default.
• W48934524 cites W1985071206 @default.
• W48934524 cites W1987124035 @default.
• W48934524 cites W1987540501 @default.
• W48934524 cites W1988730467 @default.
• W48934524 cites W1989201748 @default.
• W48934524 cites W1993103740 @default.
• W48934524 cites W1993788586 @default.
• W48934524 cites W1994488194 @default.
• W48934524 cites W1994994896 @default.
• W48934524 cites W1995067704 @default.
• W48934524 cites W1995421692 @default.
• W48934524 cites W1997231493 @default.
• W48934524 cites W2000388899 @default.
• W48934524 cites W2001511715 @default.
• W48934524 cites W2005703693 @default.
• W48934524 cites W2009683816 @default.
• W48934524 cites W2013308385 @default.
• W48934524 cites W2014753426 @default.
• W48934524 cites W2015484731 @default.
• W48934524 cites W2019527978 @default.
• W48934524 cites W2019917846 @default.
• W48934524 cites W2021619054 @default.
• W48934524 cites W2023098198 @default.
• W48934524 cites W2023214762 @default.
• W48934524 cites W2024060531 @default.
• W48934524 cites W2024127739 @default.
• W48934524 cites W2024978924 @default.
• W48934524 cites W2025500642 @default.
• W48934524 cites W2026108322 @default.
• W48934524 cites W2027068156 @default.
• W48934524 cites W2029816817 @default.
• W48934524 cites W2031605731 @default.
• W48934524 cites W2032232628 @default.
• W48934524 cites W2032316237 @default.
• W48934524 cites W2032465662 @default.
• W48934524 cites W2032888785 @default.
• W48934524 cites W2033352443 @default.
• W48934524 cites W2035001179 @default.
• W48934524 cites W2038253697 @default.
• W48934524 cites W2038403187 @default.
• W48934524 cites W2038873290 @default.
• W48934524 cites W2039101600 @default.
• W48934524 cites W2039794075 @default.
• W48934524 cites W2039913641 @default.
• W48934524 cites W2042044648 @default.
• W48934524 cites W2042476269 @default.
• W48934524 cites W2044657431 @default.
• W48934524 cites W2046822565 @default.
• W48934524 cites W2047202559 @default.
• W48934524 cites W2047738602 @default.
• W48934524 cites W2048797084 @default.
• W48934524 cites W2049300245 @default.
• W48934524 cites W2051496577 @default.
• W48934524 cites W2052602889 @default.
• W48934524 cites W2056011822 @default.
• W48934524 cites W2056802356 @default.
• W48934524 cites W2056958154 @default.
• W48934524 cites W2058495661 @default.
• W48934524 cites W2060999372 @default.
• W48934524 cites W2061936538 @default.
• W48934524 cites W2062009764 @default.
• W48934524 cites W2062334428 @default.
• W48934524 cites W2062523101 @default.
• W48934524 cites W2062921091 @default.
• W48934524 cites W2062972447 @default.
• W48934524 cites W2063717165 @default.
• W48934524 cites W2066850705 @default.
• W48934524 cites W2066927637 @default.
• W48934524 cites W2068981833 @default.
• W48934524 cites W2069671092 @default.
• W48934524 cites W2069697210 @default.
• W48934524 cites W2071444434 @default.

• next