Solving Topology Optimization Problems Using Wavelet Approximations

Volume 2: 24th Design Automation Conference ◽

10.1115/detc98/dac-5618 ◽

1998 ◽

Author(s):

Giuseppe C. A. DeRose ◽

Alejandro R. Díaz

Keyword(s):

Finite Element ◽

Topology Optimization ◽

Finite Element Methods ◽

Condition Number ◽

Optimization Problems ◽

Mesh Size ◽

Elasticity Problem ◽

New Method ◽

Galerkin Scheme

Abstract A new method to solve topology optimization problems is discussed. This method is based on the use of a Wavelet-Galerkin scheme to solve the elasticity problem associated with each iteration of the topology optimization sequence. Typically, finite element methods are used for this analysis. However, as the mesh size grows, the computational requirements necessary to solve the finite element equations increase beyond the capacity of current desk top computers. This problem is inherent to finite element methods, as the condition number of finite element matrices increases with mesh size. Wavelet-Galerkin techniques are used to replace standard finite element methods in an attempt to alleviate this problem. Examples demonstrating the performance of the new methodology are presented.

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Design and Research of Double-Drum Winch with Anti-Pressure Wheel

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.479-481.1709 ◽

2012 ◽

Vol 479-481 ◽

pp. 1709-1713

Author(s):

Kai An Yu ◽

Tao Yang ◽

Chang Zhi Gong

Keyword(s):

Finite Element ◽

Bearing Capacity ◽

Finite Element Methods ◽

Design Method ◽

New Method

In view of the problems of large stress and severe bearing heating in double-drum winch at present, this paper adopted a new method to enhance bearing capacity for double-drum winch by adding anti-pressure wheels between two drums. Finite element methods were used to analyze the strength of 4000kN-traction double-drum winches with anti-pressure wheels and without anti-pressure wheels respectively. The results of the analysis revealed that the stress of the cylinder bearing decreased from 264MPa to 167MPa. The new method by adding anti-pressure wheels had remarkably improved the endurance of the bearing. Therefore, the design method can be widely used in large-traction double-drum winch.

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Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems

Journal of Scientific Computing ◽

10.1007/s10915-020-01349-z ◽

2020 ◽

Vol 85 (2) ◽

Cited By ~ 1

Author(s):

R. Abgrall ◽

J. Nordström ◽

P. Öffner ◽

S. Tokareva

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Discontinuous Galerkin ◽

Finite Element Methods ◽

Main Idea ◽

Galerkin Methods ◽

Exact Integration ◽

Galerkin Scheme ◽

Continuous Galerkin ◽

Continuous Galerkin Methods

AbstractIn the hyperbolic community, discontinuous Galerkin (DG) approaches are mainly applied when finite element methods are considered. As the name suggested, the DG framework allows a discontinuity at the element interfaces, which seems for many researchers a favorable property in case of hyperbolic balance laws. On the contrary, continuous Galerkin methods appear to be unsuitable for hyperbolic problems and there exists still the perception that continuous Galerkin methods are notoriously unstable. To remedy this issue, stabilization terms are usually added and various formulations can be found in the literature. However, this perception is not true and the stabilization terms are unnecessary, in general. In this paper, we deal with this problem, but present a different approach. We use the boundary conditions to stabilize the scheme following a procedure that are frequently used in the finite difference community. Here, the main idea is to impose the boundary conditions weakly and specific boundary operators are constructed such that they guarantee stability. This approach has already been used in the discontinuous Galerkin framework, but here we apply it with a continuous Galerkin scheme. No internal dissipation is needed even if unstructured grids are used. Further, we point out that we do not need exact integration, it suffices if the quadrature rule and the norm in the differential operator are the same, such that the summation-by-parts property is fulfilled meaning that a discrete Gauss Theorem is valid. This contradicts the perception in the hyperbolic community that stability issues for pure Galerkin scheme exist. In numerical simulations, we verify our theoretical analysis.

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