ALBERT — All Library Books, journals and Electronic Records Telegrafenberg

1

Electronic Resource

Design optimisation of a semi-solid tyre using response surface approximations (1999)

Roux, W.J. ; Preez, R.J. du ; Stander, N.

Bradford : Emerald

Engineering computations 16 (1999), S. 165-184

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ISSN: 0264-4401

Source: Emerald Fulltext Archive Database 1994-2005

Topics: Technology

Notes: A general approach for the construction of global approximations to structural behaviour using response surface methodology is presented. The computation and use of these approximations are demonstrated using a semi-solid tyre example. The use of these global approximations to the responses made it viable to utilise the capabilities of non-linear analysis software in design optimisation. The insight gained from a preliminary low fidelity model was utilized in a two-stage approach to achieve the maximum benefit from a more expensive high fidelity model. The resulting high-accuracy approximations greatly reduced the cost of subsequent design calculations such as multidisciplinary and discrete optimisation.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1108/02644409910257449

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2

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Performance comparison of SAM and SQP methods for structural shape optimization (1996)

Barthold, F. -J. ; Stander, N. ; Stein, E.

Springer

Structural and multidisciplinary optimization 11 (1996), S. 102-112

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ISSN: 1615-1488

Source: Springer Online Journal Archives 1860-2000

Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Notes: Abstract This paper presents a numerical performance comparison of a modern version of the well-established sequential quadratic programming (SQP) method and the more recent spherical approximation method (SAM). The comparison is based on the application of these algorithms to examples with nonlinear objective and constraint functions, among others: weight minimization problems in structural shape optimization. The comparison shows that both the SQP and SAM-algorithms are able to converge to accurate minimum weight values. However, because of the lack of a guaranteed convergence property of the SAM method, it exhibits an inability to consistently converge to a fine tolerance. This deficiency is manifested by the appearance of small oscillations in the neighbourhood of the solution.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01376852

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3

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Optimization of a sheet metal forming process using successive multipoint approximations (1999)

Kok, S. ; Stander, N.

Springer

Structural and multidisciplinary optimization 18 (1999), S. 277-295

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ISSN: 1615-1488

Source: Springer Online Journal Archives 1860-2000

Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Notes: Abstract An automated optimization method based on multipoint approximations and applied to the design of a sheet metal forming process is presented. Due to the highly complex nature of the design functions, it was decided to focus on the characterization of the final product thickness distribution as a function of the preforming die shape variables. This was achieved by constructing linear approximations to the noisy responses usingresponse surface methodology (RSM). These approximations are used to obtain an approximate solution to an optimization problem. Successive approximations are constructed, which improve the solution. An automated panning-zooming scheme is used to resize and position the successive regions of approximation. The methodology is applied to optimally design the preforming die shape used in the manufacture of an automotive wheel centre pressing from a sheet metal blank. The die shape is based on a cubic spline interpolation and the objective is to minimize the blank weight, subject to minimum thickness constraints. A weight saving of up to 9.4% could be realized for four shape variables. Restart is introduced to escape local minima due to the presence of noise and to accelerate the progress of the optimization process.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01223312

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4

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The genetic algorithm applied to stiffness maximization of laminated plates: review and comparison (1998)

Potgieter, E. ; Stander, N.

Springer

Structural and multidisciplinary optimization 15 (1998), S. 221-229

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ISSN: 1615-1488

Source: Springer Online Journal Archives 1860-2000

Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Notes: Abstract The design of laminated structures is highly tailorable owing to the large number of available design variables, thereby requiring an optimization method for effective design. Furthermore, in practice, the design problem translates to a discrete global optimization problem which requires a robust optimization method such as the genetic algorithm. In this paper, the genetic algorithm, based on the real variable coding, is applied to the strain energy minimization of rectangular laminated composite plates. The results for both a point load and uniformly distributed load compare well with those achieved using trajectory methods for continuous global optimization.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01203535

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5

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A pseudo-discrete rounding method for structural optimization (1996)

Groenwold, A. A. ; Stander, N. ; Snyman, J. A.

Springer

Structural and multidisciplinary optimization 11 (1996), S. 218-227

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ISSN: 1615-1488

Source: Springer Online Journal Archives 1860-2000

Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Notes: Abstract A new heuristic method aimed at efficiently solving the mixed-discrete nonlinear programming (MDNLP) problem in structural optimization, and denotedselective dynamic rounding, is presented. The method is based on the sequential rounding of a continuous solution and is in its current form used for the optimal discrete sizing design of truss structures. A simple criterion based on discrete variable proximity is proposed for selecting the sequence in which variables are to be rounded, and allowance is made for both upward and downward rounding. While efficient in terms of the required number of function evaluations, the method is also effective in obtaining a low discrete approximation to the global optimum. Numerical results are presented to illustrate the effectiveness and efficiency of the method.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01197037

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6

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Optimal discrete sizing of truss structures subject to buckling constraints (1997)

Groenwold, A. A. ; Stander, N.

Springer

Structural and multidisciplinary optimization 14 (1997), S. 71-80

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ISSN: 1615-1488

Source: Springer Online Journal Archives 1860-2000

Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Notes: Abstract The selective dynamic rounding (SDR) algorithm previously developed by the authors, and based on a dual step rounding approach, is used for the optimal sizing design of truss structures subject to linear buckling constraints. The algorithm begins with a continuous optimum followed by a progressive freezing of individual variables while solving the remaining continuous problems. The allowable member stresses are predicted by the linear regression of the tabular section properties, while the exact allowable compressive stresses are back-substituted for those variables fixed on discrete values in each intermediate mixed-discrete nonlinear problem. It is shown that a continuous design based on the regression analysis of section effectiveness vs. area is effective as a starting point for the dual step discrete optimization phase. A range of examples is used to illustrate that with “conservative” regression, discrete designs can be achieved which are significantly lighter than those in which the variables have been rounded up.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01812508

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7

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Structural optimization using augmented Lagrangian methods with secant Hessian updating (1996)

Coster, J. E. ; Stander, N.

Springer

Structural and multidisciplinary optimization 12 (1996), S. 113-119

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ISSN: 1615-1488

Source: Springer Online Journal Archives 1860-2000

Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Notes: Abstract The performance of a new implementation of the augmented Lagrangian method is evaluated on a range of explicit and structural sizing optimization problems. The results are compared with those obtained using other mathematical programming methods. The implementation uses a first-order Lagrange multiplier update and the Hessian of the augmented Lagrangian function is approximated using partitioned secant updating. A number of different secant updates are evaluated. The results show the formulation to be superior to other implementations of augmented Lagrangian methods reported in the literature and that, under certain conditions, the method approaches the performance of the state-of-the-art SQP and SAM methods. Of the secant updates, the symmetric-rank-one update, is superior to the other updates including the BFGS scheme. It is suggested that the individual function, secant updating employed may be usefully applied in contexts where structural analysis and optimization are performed simultaneously, as in the simultaneous analysis and design method. In such cases the functions are partially separable and the associated Hessians are of low rank.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01196943

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8

Electronic Resource

FEASIBLE DESCENT CONE METHODS FOR INEQUALITY CONSTRAINED OPTIMIZATION PROBLEMS (1996)

SNYMAN, J. A. ; STANDER, N.

Chichester [u.a.] : Wiley-Blackwell

International Journal for Numerical Methods in Engineering 39 (1996), S. 1341-1356

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ISSN: 0029-5981

Keywords: constrained optimization ; feasible descent ; mathematical programming ; Engineering ; Engineering General

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics , Technology

Notes: A new Feasible Descent Cone (FDC) method for constrained optimization, previously restricted to linear objectives, is here generalized to include non-linear objective functions as well. In the basic and exact algorithm a sequence of descent steps is taken through the interior of the feasible region along the central lines of mathematically defined descent cones, constructed at successive boundary points. Here the basic algorithm is modified to allow for a minimum to occur within the interior, along a central descent ray in the case of non-linear objectives. A special interior procedure, with desirable mathematical properties, is adopted should the latter occur. To ensure economic implementation, the new generalized and exact algorithm, referred to as SSOPT2, is successively applied to a sequence of approximate quadratic subproblems. The overall generalized procedure that includes the successive application of SSOPT2 to the approximate subproblems, is referred to as the successive approximation version 2 algorithm (SAM2). The practical performance of SAM2 is assessed through its application to a number of small but otherwise representative test problems.

Additional Material: 2 Ill.

Type of Medium: Electronic Resource

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