Minimum mass design of elastic frames subjected to multiple load cases

Pedersen, Pauli; Jørgensen, L. W.

doi:10.1016/0045-7949(84)90090-7

Cited by 19 publications

(2 citation statements)

References 5 publications

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“…The model of Tada and Seguchi (1989) is similar in spirit to a classical approach in engineering design to dealing with varying external forces, which is known as the multi-load case of the structural optimization problem (e.g., Pedersen and Jørgensen, 1984). Such an approach seeks to take different load cases into account in the model by, essentially, considering the worst-case scenario for each set of design parameter values.…”

Section: The Deterministic Problemmentioning

confidence: 99%

Stochastic bilevel programming in structural optimization

Christiansen¹,

Patriksson²,

Wynter

2001

Structural and Multidisciplinary Optimization

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We consider the mathematical modelling and solution of robust and cost-optimizing structural (topology) design problems. The setting is the optimal design of a linear-elastic structure, for example a truss topology, under unilateral frictionless contact, and under uncertainty in the data describing the load conditions, the material properties, and the rigid foundation. The resulting stochastic bilevel optimization model finds a structural design that responds the best to the given probability distribution in the data. This model is of special interest when a structural failure will lead to a reconstruction cost, rather than loss of life.For the mathematical model, we provide results on the existence of optimal solutions which allow for zero lower design bounds. We establish that the optimal solution is continuous in the design bounds, a result which validates the use of small but positive values of them, and for such bounds we also establish the locally Lipschitz continuity and directional differentiability of the implicit one-level objective function. We also provide a simple algorithm for the solution of the problem, which makes use of its differentiability properties and parallelization strategies across the scenarios. A small set of numerical experiments illustrates the behaviour of the stochastic solution compared to an average-case deterministic one, establishing an increased robustness.

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Section: The Deterministic Problemmentioning

confidence: 99%

Stochastic bilevel programming in structural optimization

Christiansen¹,

Patriksson²,

Wynter

2001

Structural and Multidisciplinary Optimization

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“…Numerical structural optimization of frame structures dates back to as early as the 1960s. More recent articles proposing sizing optimization of frames under Timoshenko beam assumptions are, eg, Pedersen and Jørgensen and Cameron et al An important application related to the automotive industry is optimal design of frames for crash‐worthiness. An approach for this application based on topology optimization is presented in Pedersen …”

Section: Introductionmentioning

confidence: 99%

Conceptual jacket design by structural optimization

2018

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We present an approach for sizing optimization of jacket structures and apply it to investigate the conceptual design of jackets for offshore wind turbines. Conceptual design is an input to early structural and financial models, and we assume simplified analysis and load models. A four‐legged jacket for the DTU 10‐MW wind turbine in 50‐m water depth is modelled by Timoshenko beam finite elements, and the structural dimensions of the beam cross sections are considered as continuous design variables. A structural optimization problem is formulated to minimize the jacket mass, with constraints on fatigue and ultimate limit states. The optimal design problem is then used to investigate how the optimized mass depends on the number of bays and the jacket leg distance. The conceptual design investigation led to a new conceptual design with 14% lower mass compared with the original conceptual design. We conclude that structural optimization can provide useful insights in the conceptual design phase and lead to a better starting point for the further design and planning processes.

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An algorithm for the optimum design of braced and unbraced steel frames under earthquake loading

Gülay

Boduroglu

1989

Earthq Engng Struct Dyn

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SUMMARYA solution technique based on the sequential linear programming (SLP) method is presented for the optimum design of braced and unbraced steel frames in seismic regions. First, the optimum rigidity distribution of the frames under static loading is computed, then the optimization procedure is repeated under the combined loading, setting lower bounds on the optimum static cross-sectional areas and increasing allowable stresses.The stiffness, stress, displacement and side constraints are included in the optimization problem. As a result, a highly non-linear mathematical programming problem is produced. A non-linear programming algorithm is offered for the solution which is based on the successive linearization of non-linear expressions and employs the simplex routine in an iterative manner.Design variables are chosen to be the free nodal displacements and the cross-sectional areas of the members, while the objective function is taken to be the minimization of the total volume of the structure.As numerical applications, optimum weights of several frames (unbraced, concentrically and eccentrically braced) under static and combined loading cases are computed and the results are compared with those available in the literature.

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Minimum mass design of elastic frames subjected to multiple load cases

Cited by 19 publications

References 5 publications

Stochastic bilevel programming in structural optimization

Stochastic bilevel programming in structural optimization

Conceptual jacket design by structural optimization

An algorithm for the optimum design of braced and unbraced steel frames under earthquake loading

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