A constrained optimization approach to finite element mesh smoothing

Parthasarathy, V.; Kodiyalam, Srinivas

doi:10.1016/0168-874x(91)90004-i

Cited by 110 publications

(55 citation statements)

References 6 publications

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“…The aspect ratio (AR) is the ratio of the shortest to the longest side in a mesh cell. It should be equal to 1 for ideal results [32]. In the meshed collector without glass the total elements produced were 41510 and the trough with glass cover had 57516 elements.…”

Section: B Mesh Generationmentioning

confidence: 99%

Design, Simulation and Manufacturing of an Integrated Composite Material Parabolic Trough Solar Collector

Abdel-Hady¹,

Shakil²,

Hamed³

et al. 2016

IJET

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Abstract-Design, simulation, and manufacturing process of an integrated thermal photovoltaic closed parabolic collector (ITPVCPC) using composite material is presented in this paper. The design includes two flanges for supporting photovoltaic panels. Two cases of troughs were designed and studied, one with glass cover over the aperture area and another without it in order to investigate the structure rigidity and solar ray collection in the absorber tube. Three-dimensional modelling and structural finite element analysis (FEA) based simulation was done for the design. In the simulation, the ITPVCPC structure was subjected to the upper limits of wind pressure and temperature-rise loadings similar to the real working conditions. Optical analysis was done for the trough to study the effect of structure deformation on solar ray collection. The glass covered ITPVCPC showed higher structure deformation than the one without glass. Glass fiber with polyester resin was used in the manufacture of ITPVCPC for its low price compared to other composite materials. The study shows that glass fiber (with polyester matrix) is an ideal composite material for ITPVCPC for its high rigidity, low cost, and ease of manufacture. This design is successfully implemented and is the source of thermal and electrical power for a solar desalination system installed in Jeddah, Saudi Arabia. Keywords: Finite element analysis (FEA), concentrating solar power (CSP), hand-layup method, glass fiber reinforced polymer (GFRP) I.INTRODUCTION Fossil fuels such as petroleum oil, coal and natural gas are used as a primary energy source in developed nations. These carbon rich fuels release CO2 to the environment which has a negative effect on the atmosphere. It alters the radiation-balance of the earth and promotes global warming [1]. This has forced the consumers to think of alternate sources which would be cheap at least in the long run. Due to awareness of pollution and economics of fuel, the focus is now shifted to solar and other clean energy sources. Parabolic trough technology is currently the lowest-cost concentrating solar power (CSP) technology for electricity production [2]. Parabolic trough collector (PTC) uses a highly reflective surface to focus incident solar rays on a heat collector element (HCE) also called receiver tube. The receiver tube is placed at the point of convergence (focal point of parabola). The tube contains a working fluid that absorbs solar heat and gets heated up to temperatures of 350o C or more. It is enveloped by an evacuated (vacuumed) glass tube to reduce convective heat loss to the surrounding. The collector has a disadvantage of smaller angle of view. Therefore, to maximize the solar heat gain, a tracking mechanism is used to align it with respect to the changing position of the sun. Collector is being considered for a lot of applications like Enhanced Oil Recovery (EOR) [3], water disinfection in third world countries [4], desalination [5], refrigeration and cooling [6], heating applications [7] etc. Many innovativ...

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Section: B Mesh Generationmentioning

confidence: 99%

Design, Simulation and Manufacturing of an Integrated Composite Material Parabolic Trough Solar Collector

Abdel-Hady¹,

Shakil²,

Hamed³

et al. 2016

IJET

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“…Heuristically based membership functions, 4. Membership functions based on statistics or probability density functions [12]. In this paper, we concern with human concept based membership function.…”

Section: Fig 10 Input Membership Functionsmentioning

confidence: 99%

“…For this process, the first triangle is constructed as equilateral triangle. The next step is to compute angles α, β and distances d 1 …”

Section: Fig 10 Input Membership Functionsmentioning

confidence: 99%

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A Method Based on Fuzzy Logic Technique for Smoothing in 2D

Çınar

2004

Computational Science - ICCS 2004

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Abstract. This paper describes a novel approach based on fuzzy logic technique for smoothing process on the unstructured meshes in 2D. The proposed method works local on triangulation. Therefore, remeshing does not require. It is known that other smoothing operations such as laplacian smoothing , optimization based smoothing, angle based smoothing, and hybrid smoothing operations work global. That is, in these methods, meshing is achieved, afterwards remeshing is done for smoothing. Whereas, the goal of presented method is to find the best fit location of node while meshing is done. However, remeshing process is avoided.

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“…Many mathematical techniques have been proposed for improving poor quality meshes. These include methods for improving the mesh even as it is generated (vertex insertion/deletion) [16] and postprocessing methods in which mesh topology is modified (edge or element swapping) [9,6] and/or vertex coordinates are modified (smoothing or optimization of an objective function that measures mesh quality) [3,5,7,10,14,17,4]. The latter set of methods are sometimes referred to as node-movement methods.…”

Section: Background and Introductionmentioning

confidence: 99%

Incorporating the min-max mesh optimization method within the Target-Matrix Paradigm.

Knupp¹,

Day²

2012

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The Target-Matrix Optimization Paradigm (TMOP) is a method for improving mesh quality via node movement [11]. Through the use of appropriate pre-defined quality metrics and Target-matrices, TMOP provides the ability to define mesh quality in terms of element shape, volume, and edge orientation as a function of position within the mesh, thus facilitating high-level goals such as size-adapted meshing. The Paradigm is developed further in this paper by showing how it can be applied to the problem of improving the mesh in locations where the quality is the worst. Improving the worst quality portions of a mesh was investigated by Freitag [8], Amenta [1], and others, who showed that the problem can be formulated as a min-max optimization problem. The Target-paradigm is used to extend the previous work in two important respects. First, by using quality metrics from the Targetparadigm, quality can be user-specified via Target-matrices instead of the quality definition being hard-wired into the quality metric. Second, by making use of the sample point concept in TMOP, one can extend min-max mesh optimization to non-simplicial element types such as quadrilaterals. Numerical experiments were performed to illustrate these extensions and to investigate their utility. A non-gradient solver known as the amoeba was used to numerically compute the optimal solutions. This derivative-free method, in conjunction with the use of barrier metrics from TMOP, enables the solution of the min-max problem without the use of explicit constraints to guarantee that the optimal mesh is non-inverted. The experiments showed that the use of Target-metrics in min-max with triangle (or tetrahedral) element meshes is able to effectively improve the worst quality elements in terms of shape or in terms of size+shape. The experiments also showed that the mesh min-max extension 3 to quadrilateral element meshes can lead to acceptable meshes using barrier metrics from the Target-paradigm, provided that inter-element mesh smoothness is not important. Poor behavior was observed when using non-barrier Target-metrics in min-max with quadrilateral element meshes. For both simplicial and quadrilateral meshes, the min-sum method can be competitive with min-max, however.4

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A constrained optimization approach to finite element mesh smoothing

Cited by 110 publications

References 6 publications

Design, Simulation and Manufacturing of an Integrated Composite Material Parabolic Trough Solar Collector

Design, Simulation and Manufacturing of an Integrated Composite Material Parabolic Trough Solar Collector

A Method Based on Fuzzy Logic Technique for Smoothing in 2D

Incorporating the min-max mesh optimization method within the Target-Matrix Paradigm.

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