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  • 1
    Electronic Resource
    Electronic Resource
    Evolutionary topology and shape design for general physical field problems (2000)
    Springer
    Computational mechanics 26 (2000), S. 129-139 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract  As a practical tool for design engineers, evolutionary techniques for structural topology, shape and size optimisation have successfully resolved the whole range of structural problems from frames to 2D and 3D continuums with design criteria of stress, stiffness, frequency and buckling. In view of the generality of the finite element formulation using either a variational calculus or weighted residual approach, it is logical to extend its applications to other steady state field problems in mathematical physics governed by partial differential equations. The range of physical problems falling to this category includes heat conduction, incompressible fluid flow, elastic torsion, electrostatics and magnetostatics, etc. This paper discusses the general principles involved in setting up the adaptive evolutionary algorithms that have finite element techniques as the analysis engines. To avoid the complexity of classical solutions, the proposed method develops a simple outer loop procedure consisting of finite element analysis and design modifications. Illustrative examples are presented to demonstrate the capability in solving the above-mentioned physical field situations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660000160
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  • 2
    Electronic Resource
    Electronic Resource
    On the representation of elastic displacement fields in terms of three harmonic functions (1979)
    Springer
    Journal of elasticity 9 (1979), S. 325-333 
    Details
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract In this paper the representation of displacement fields in linear elasticity in terms of harmonic functions is considered. In the original work of Papkovich and Neuber four harmonic functions were presented with a subsequent reduction to three on the grounds that only three are sufficient for the representation of displacements fields. This reduction is unsubstantiated and several authors have investigated the generality of the Papkovich-Neuber solutions. The paper derives by simple means the conditions under which it is possible to omit one of the four harmonic functions and considers the significance of the subsequent three function form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00041103
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  • 3
    Electronic Resource
    Electronic Resource
    An asymptotic formula for correcting finite element predicted natural frequencies of membrane vibration problems (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 63-73 
    Details
    ISSN: 1069-8299
    Keywords: asymptotic solution ; natural frequencies ; membrane vibrations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper an asymptotic formula has been developed to correct the discretization error for the finite element predicted natural frequencies of membrane transverse vibration problems. The general idea behind deriving this asymptotic formula is that, when the finite element size approaches zero, a discretized finite element system approaches a continuous system and the predicted natural frequencies of the system from the finite element analysis therefore approach the exact solutions of the system. Without losing generality, several different finite element mesh patterns have been considered and the same asymptotic formula for correcting the finite element predicted natural frequency has been obtained for all the different mesh patterns because of the uniqueness of the exact solution to the natural frequency of a real structure. The usefulness, effectiveness and efficiency of the present asymptotic formula have been assessed by a simple but critical problem, for which the exact solution is available for comparison. In order to investigate the applicability of the asymptotic formula to practical engineering problems, two challenging membrane vibration problems of irregular shapes, an L-shape and a tapered shape with a circular hole in the centre, have also been analysed. The related numerical results have demonstrated that the asymptotic formula provides a very useful post-processing error corrector for the finite element predicted natural frequencies of membrane transverse vibration problems, even though the problem domains are of irregular shape. The greatest advantage in using the present asymptotic formula is that it yields a solution of higher accuracy, by simply using the formula to correct the rough solution obtained from a much coarser finite element mesh with fewer degrees of freedom, without any further finite element calculation.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Explicit formulas for correcting finite-element predictions of natural frequencies (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 671-680 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Explicit formulas for correcting finite-element predictions of natural frequencies are presented for longitudinal, torsional and bending vibrations of beams. By employing these simple explicit formulas the finite-element discretization error in the natural frequency predictions can be effectively reduced at almost no computational cost. For longitudinal and torsional vibrations the frequency correction always yields the exact solution, while for the bending vibration it gives a significant improvement over the uncorrected frequencies. This method is also applied to two- and three-dimensional frames, and it is found that the errors in the original finite-element predictions of natural frequencies are reduced by about 50 per cent after such a correction.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090806
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  • 5
    Electronic Resource
    Electronic Resource
    Instability, chaos, and growth and decay of energy of time-stepping schemes for non-linear dynamic equations (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 393-401 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we present numerical experiments made to investigate the behaviour of the Newmark time-stepping scheme applied to non-linear dynamic systems. Our attention is focused on the instability and chaos in the Newmark scheme when it is applied to the equation ü + P(u) = 0, representing a non-linear elastic spring. Some unusual modes of behaviour, which are of substantial interest, have been observed. In the first case, a stable but chaotic solution is found. In the second case, while a stable solution is obtained with a certain time step, an unstable solution is found by decreasing the time step. In the third case, instability is triggered by neglecting the initial acceleration. A simple modification of the Newmark scheme is proposed which keeps the energy constant for the equation ü + P(u) = 0 and thereby guarantees unconditional stability. Numerical examples in support of such an energy-conserving scheme are presented.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100505
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  • 6
    Electronic Resource
    Electronic Resource
    Analytical solutions of mass transport problems for error estimation of finite/infinite element methods (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 13-23 
    Details
    ISSN: 1069-8299
    Keywords: mass transport problems ; error estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In order to make an exact estimation of discretization error for finite/infinite element methods, it is necessary to develop analytical solutions for some transient mass transport problems in infinite media. These transient mass transport problems may be viewed as the benchmark problems for the discretization error estimation of a new numerical method so that they generally have the following characteristics: (1) their initial and boundary conditions can be exactly modelled by the finite/infinite element method; (2) their solutions can be rigorously expressed in a closed form. In this paper, several of the aforementioned problems have been constructed and solved mathematically for transient mass transport problems in both 1D and 2D infinite media.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110104
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  • 7
    Electronic Resource
    Electronic Resource
    Evolutionary natural frequency optimization of thin plate bending vibration problems (1996)
    Springer
    Structural and multidisciplinary optimization 11 (1996), S. 244-251 
    Details
    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 extends the evolutionary structural optimization method to the solution for maximizing the natural frequencies of bending vibration thin plates. Two kinds of constraint conditions are considered in the evolutionary structural optimization method. If the weight of a target structure is set as a constraint condition during the natural frequency optimization, the optimal structural topology can be found by removing the most ineffectively used material gradually from the initial design domain of a structure until the weight requirement is met for the target structure. However, if the specific value of a particular natural frequency is set as a constraint condition for a target structure, the optimal structural topology can be found by using a design chart. This design chart describes the evolutionary process of the structure and can be generated by the information associated with removing the most inefficiently used material gradually from the initial design domain of a structure until the minimum weight is met for maintaining the integrity of a structure. The main advantage in using the evolutionary structural optimization method lies in the fact that it is simple in concept and easy to be included into existing finite element codes. Through applying the extended evolutionary structural optimization method to the solution for the natural frequency optimization of a thin plate bending vibration problem, it has been demonstrated that the extended evolutionary structural optimization method is very useful in dealing with structural topology optimization problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01197040
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  • 8
    Electronic Resource
    Electronic Resource
    An evolutionary method for optimal design of plates with discrete variable thicknesses subject to constant weight (1999)
    Springer
    Structural and multidisciplinary optimization 17 (1999), S. 55-64 
    Details
    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 simple evolutionary method for optimization of plates subject to constant weight, where design variable thicknesses are discrete. Sensitivity numbers for sizing elements are derived using optimality criteria methods. An optimal design with minimum displacement or minimum strain energy is obtained by gradually shifting material from elements to the others according to their sensitivity numbers. A simple smoothing technique is additionally employed to suppress formation of checkerboard patterns. It is shown that the proposed method can directly deal with discrete design variables. Examples are provided to show the capacity of the proposed evolutionary method for structural optimization with discrete design variables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01197713
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  • 9
    Electronic Resource
    Electronic Resource
    On equivalence between stress criterion and stiffness criterion in evolutionary structural optimization (1999)
    Springer
    Structural and multidisciplinary optimization 18 (1999), S. 67-73 
    Details
    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 In a finite element analysis (FEA), the contours of element von Mises stress and stiffness sensitivity number are found to be very similar. This paper shows there to be an equivalence between the von Mises stress criterion and the stiffness criterion for element elimination or addition in evolutionary structural optimization. The examples presented demonstrate the same resulting topologies during the evolving process using the two “different” criteria. The effect of numerical errors on topology is also investigated. It is concluded that the optimized topologies of a structure using the fully stressed criterion and the minimum compliance or maximum stiffness criterion are equivalent.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01210693
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  • 10
    Electronic Resource
    Electronic Resource
    3D and multiple load case bi-directional evolutionary structural optimization (BESO) (1999)
    Springer
    Structural and multidisciplinary optimization 18 (1999), S. 183-192 
    Details
    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 Evolutionary Structural Optimization (ESO), is a numerical method of structural optimization that is integrated with finite element analysis (FEA). Bi-directional ESO (BESO) is an extension to this method and can begin with minimal amount of material (only that necessary to support the load and support cases) in contrast to ESO which uses an initially oversized structure. Using BESO the structure is then allowed to grow into the optimum design or shape by both adding elements where the stresses are the highest and taking elements away where stresses are the lowest. In conducting this research, a methodology was developed (and integrated into the ESO program EVOLVE) which produced the optimal 3D finite element models of a structure in a more reliable way than the traditional ESO method. Additionally, the BESO method was successfully extended to multiple load cases for both 2D and 3D. Two different algorithms were used to find the best structure experiencing more than one load case and the results of each are included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01195993
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