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  • 1
    Electronic Resource
    Electronic Resource
    A smoothing scheme for a minimum weight problem in structural plasticity (1999)
    Springer
    Structural optimization 17 (1999), S. 279-285 
    Details
    ISSN: 0934-4373
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract We revisit an important and challenging class of minimum weight structural plasticity problems, the feature of which is the presence of complementarity constraints. Such relations mathematically express the perpendicularity of two sign-constrained vectors and mechanically describe an inherent property of plasticity. The optimization problem in point is referred to in the mathematical programming literature as a Mathematical Program with Equilibrium Constraints (MPEC). Due to its intrinsic complexity, MPECs are computationally very hard to solve. In this paper, we adopt recent ideas, proposed by mathematical programmers, on smoothing to develop a simple scheme for reformulating and solving our minimum weight problem as a standard nonlinear program. Simple examples concerning truss-like structures are also presented for illustrative purpose.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01207004
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    On the numerical solution of a class of unilateral contact structural optimization problems (1999)
    Springer
    Structural optimization 17 (1999), S. 155-161 
    Details
    ISSN: 0934-4373
    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 deals with a special class of structural optimization problems in nonsmooth mechanics. More precisely, it is required to minimize the weight of a structure subject to frictionless unilateral contact conditions and constraints on the magnitudes of contact forces, displacements, stresses and cross-sectional areas. This problem, as is well-known, can be formulated as a special and challenging optimization problem known as a Mathematical Program with Equilibrium Constraints (MPEC), a key feature of which is the presence of complementarity conditions, involving the orthogonality of two sign-constrained vectors. In spite of its inherent nonsmoothness, we attempt to solve the problem using standard nonlinear programming techniques. In particular, we investigate numerically the application of two simple algorithms, both based on the use of the general-purpose nonlinear programming code CONOPT accessed via the powerful GAMS modelling language, for solving the suitably reformulated problem. Application is illustrated by means of three numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01195940
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    On multiplicity of solutions in quasi-brittle fracture computations (1997)
    Springer
    Computational mechanics 19 (1997), S. 511-516 
    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 The analysis of quasi-brittle fracture processes is formulated as a linear complementarity problem either in finite increments or in rates. Some time-stepping solution procedures and mathematical programming algorithms are discussed as for their ability to capture the whole set of possible alternative equilibrium paths. Potentialities and limitations of the proposed approach and of the relevant procedures are pointed out also by means of a numerical example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050201
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    A smoothing scheme for a minimum weight problem in structural plasticity (1999)
    Springer
    Structural and multidisciplinary optimization 17 (1999), S. 279-285 
    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 We revisit an improtant and challenging class of minimum weight structural plasticity problems, the feature of which is the presence of complementarity constraints. Such relations mathematically express the perpendicularity of two sign-constrained vectors and mechanically describe an inherent property of plasticity. The optimization problem in point is referred to in the mathematical programming literature as a Mathematical Program with Equilibrium Constraints (MPEC). Due to its intrinsic complexity, MPECs are computationally very hard to solve. In this paper, we adopt recent ideas, proposed by mathematical programmers, on smoothing to develop a simple scheme for reformulating and solving our minimum weight problem as a standard nonlinear program. Simple examples concerning truss-like structures are also presented for illustrative purposes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01207004
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Optimum shakedown design under residual displacement constraints (2000)
    Springer
    Structural and multidisciplinary optimization 19 (2000), S. 130-139 
    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. We consider the minimum weight design of suitably discretized elastoplastic structures subjected to variable repeated loads and constraints on the amount of residual (or permanent) deflections. The optimization problem is formulated on the basis of the classical lower bound theorem of shakedown, supplemented by appropriate constraints on deflections obtained from existing bounding results. The primary purpose of the paper is to show that, even for large size structures, this important and challenging problem can be modeled and solved directly as a mathematical programming problem within the industry standard modeling framework GAMS. Examples concerning truss-like structures are presented for illustrative purposes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001580050093
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    On the numerical solution of a class of unilateral contact structural optimization problems (1999)
    Springer
    Structural and multidisciplinary optimization 17 (1999), S. 155-161 
    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 deals with a special class of structural optimization problems in nonsmooth mechanics. More precisely, it is required to minimize the weight of a structure subject to frictionless unilateral contact conditions and constraints on the magnitudes of contact forces, displacements, stresses and cross-sectional areas. This problem, as is well-known, can be formulated as a special and challenging optimization problem known as a Mathematical Program with Equilibrium Constraints (MPEC), a key feature of which is the presence of complementarity conditions, involving the orthogonality of two sign-constrained vectors. In spite of its inherent nonsmoothness, we attempt to solve the problem using standard nonlinear programming techniques. In particular, we investigate numerically the application of two simple algorithms, both based on the use of the general-purpose nonlinear programming code CONOPT accessed via the powerful GAMS modelling language, for solving the suitably reformulated problem. Application is illustrated by means of three numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01195940
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    LARGE DISPLACEMENT ELASTOPLASTIC ANALYSIS OF SEMIRIGID STEEL FRAMES (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 741-762 
    Details
    ISSN: 0029-5981
    Keywords: elastoplastic analysis ; mathematical programming ; plasticity ; semirigid connections ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mathematical programming approach for the large displacement analysis of elastoplastic plane frames with flexible, partial-strength beam-to-column connections is proposed. The incremental formulation is developed within the framework of a discrete model, piecewise linear yield surfaces and large displacement theory. It is based on the fundamental relations of equilibrium, compatibility and constitutive laws, all expressed in incremental form. The irreversible plasticity laws are used in a stepwise holonomic format. A feature of the final mathematical programming problem, known as a non-linear complementarity problem, is that the governing relations exhibit symmetry as a result of the use of fictitious quantities and non-linear residuals. The iterative predictor-corrector computational scheme adopted has the ability of tracing historically a sequence of plastic hinge activations and/or unloadings well beyond any critical point. Numerical examples are presented to illustrate and validate the accuracy of the approach.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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