Multiparameter structural shape optimization by the finite element method

Dems, K.; Mróz, Z.

doi:10.1002/nme.1620130204

Cited by 56 publications

(13 citation statements)

References 15 publications

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“…The results shown in Fig. 3 agree very well with the findings of Dems and Mroz [20] for an isotropic plate. It can be seen 20 that the elastic compliance has stationary conditions at three different points, at the plate's centre and two other locations offset from the plate's centre, y2.0.…”

Section: 1supporting

confidence: 87%

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Shape design sensitivity analysis with respect to the positioning of features in composite structures using the boundary element method

Tafreshi

2006

Engineering Analysis with Boundary Elements

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This paper presents the application of the boundary element method to the shape design sensitivity analysis of composite structures with holes and cutouts. A two-dimensional anisotropic domain which contains a number of voids of arbitrary shapes will be considered.The objective is to perform the design sensitivity analysis of the structure with respect to the translation and rotation of the voids using the boundary element method. A directly differentiated form of the boundary integral equation, with respect to geometric design variables is used to calculate the shape design sensitivities for anisotropic materials. The response sensitivity analysis, with respect to the design variables such as feature positions and orientations, is achieved by the definition of appropriate design velocity fields for these variables. To find the optimum positions of the features within an anisotropic structure with the highest stiffness, the elastic compliance of the structure has been minimized subject to constraints upon stresses and geometry. Due to the non-linear nature of the mean compliance and stresses, the numerical optimisation algorithm used is the feasible direction method, together with the golden section method for the one-dimensional search. A couple of test cases have been performed to verify the proposed method.

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Section: 1supporting

confidence: 87%

“…This plate with isotropic material properties, was analysed by Dems and Mroz [20]. They found the optimum position of the hole, along the direction normal to the applied load, by minimization of its elastic compliance, using the finite element method.…”

Section: 1mentioning

confidence: 99%

Shape design sensitivity analysis with respect to the positioning of features in composite structures using the boundary element method

Tafreshi

2006

Engineering Analysis with Boundary Elements

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“…The essential assumption of the "regulatory model" is the existence of homeostasis in the remodeling process, described by the distinguished value of SED. But SED (as an energy measure) is also of a prime importance in optimization research, far from biomechanical applications [26][27][28]. Pedersen [28] presented…”

Section: 2mentioning

confidence: 99%

“…But SED (as an energy measure) is also of a prime importance in optimization research, far from biomechanical applications [26,27,28]. Pedersen [28] presented the considerations of the optimization of structural shape by minimizing the strain energy.…”

Section: 2mentioning

confidence: 99%

New biomimetic approach to the aircraft wing structural design based on aeroelastic analysis

Gaweł

Nowak

Hausa

et al. 2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. This paper presents a new biomimetic approach to the structural design. For the purpose of aircraft wing design the numerical environment combining simultaneous structural size, shape, and topology optimization based on aeroelastic analysis was developed. For the design of aircraft elements the optimization process must be treated as a multi-load case task, because during the fluid structure interaction analysis each step represents a different structural load case. Also, considering different angles of attack, during the CFD computation each result is considered. The method-specific features (such as domain independence, functional configurations during the process of optimization, and multiple load case solution implemented in the optimization scenario) enable the optimal structural form. To illustrate the algorithm functionality, the problem of determining the optimal internal wing structure was presented. The optimal internal wing structure resulting from aeroelastic computation with different angles of attack has been presented. ture of a wing. Their solution computed the pressure distribution for an analyzed shape, but missed coupling. Another approach to wing optimization refers to the reduction of skin thickness, which was done by Wang and Williams [3]. The wing was divided into dozens of panels, modeled as membranes. The wing՚s weight was reduced along with the increased stiffness of the whole model, stemming from the modification of the membranes thickness.In the papers of Krog [4, 5] the optimization of Airbus A380 ribs was treated as a two-step process. Potential geometry was reduced using standard topology optimization, and then the geometrical model was created for structural optimization purposes. Finally, the optimal structure was transformed into a CAD model which was afterwards verified.Stettner and Schuhmacher [6] also referred to topological and structural optimizations for designing the rear part of a military transport aircraft fuselage. The whole assembly as well as its frame has been analyzed with the same optimization methods within a two-stage process. The results were obtained separately for bending load, torsional load, and pressure exerted on side walls. Additionally, authors attempted to compile the individual results into a single form. However, it has to be emphasized that presented solution did not result from multi-load case calculations.Maute and Allen [7] suggested implementation of structural optimization methods in combination with an aeroelastic simulation. The problem was presented on the example of a slim wing model used for the two-dimensional topological optimization. The obtained configuration presented a conceptual distribution of the material inside the wing subjected to the impact of surrounding flow. The internal structure significantly differed from one we might expect on the basis of an analysis of the regular pressure distribution over a wing surface.

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“…In Reference [3] a shape optimization problem for 3D non-linear elastic body subjected to single-static loading is considered. Structural compliance measured by the total complementary energy is minimized, value of the structural volume is considered as a prescribed one.…”

Section: Introductionmentioning

confidence: 99%

Optimization algorithms for physically non‐linear structures

Selyugin¹

2001

Numerical Meth Engineering

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SUMMARYA family of numerical methods and algorithms targeted to the optimization of physically non-linear structures is proposed. The structures are described using ÿnite element approach, they are supposed to be loaded by single static loading. It is assumed that various types of ÿnite elements are used for the description. Buckling e ects are neglected. Sizing design variables with prescribed lower limits are considered. The numerical approach is based on the use of physically non-linear hyperelastic (PNH) model for the description of active loading process for the physically non-linear structures. Three optimization sub-problems for the PNH structures are considered. Variational principles for the structures as well as optimality conditions and particular solutions of the sub-problems are used for the development of algorithms intended for numerical solution of the sub-problems. Geometrical interpretation of the algorithms is presented. Monotonicity properties of the algorithms are proved under some assumptions. It is indicated how the algorithms may be used for the general case of optimization of physically non-linear structure under single loading. Numerical examples are presented. Monotonicity of the algorithms is demonstrated. It is noted that no numerical problems arise when some structural members degenerate during numerical process.

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Multiparameter structural shape optimization by the finite element method

Cited by 56 publications

References 15 publications

Shape design sensitivity analysis with respect to the positioning of features in composite structures using the boundary element method

Shape design sensitivity analysis with respect to the positioning of features in composite structures using the boundary element method

New biomimetic approach to the aircraft wing structural design based on aeroelastic analysis

Optimization algorithms for physically non‐linear structures

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