Topology optimization in structural mechanics

Lewiński, Tomasz; Czarnecki, S.; Dzierżanowski, Grzegorz; Sokół, Tomasz

doi:10.2478/bpasts-2013-0002

Cited by 9 publications

(7 citation statements)

References 85 publications

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“…Refs. where the numerical solutions for the least weight Michell trusses are shown and paper where the GRAMP method being the new and improved version of the RAMP method has been proposed. Let us note that the above mentioned problem does not affect the optimal solutions concerning the pure pressure and pure shear cases.…”

Section: Final Remarksmentioning

confidence: 99%

The emergence of auxetic material as a result of optimal isotropic design

Czarnecki

Wawruch

2015

Physica Status Solidi (b)

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Using both mathematical and numerical methods, the optimal distributions of material characterized by the Young modulus and Poisson ratio (as well as other moduli of isotropy) maximizing the overall stiffness of an inhomogeneous isotropic elastic 3D body transmitting a given surface loading to a given support are constructed. The overall stiffness of the body is defined as the inverse of the work of external forces on displacements, called here the compliance of the structure. The isoperimetric condition bounds the integral of the trace of the Hooke tensor. It is proved that isotropic composite materials forming the bodies of extremely high stiffness exhibit negative Poisson ratio in large subdomains, which points at the significance of the auxetic material in modern structural design. The obtained results show that the whole range of possible variation of the Poisson ratio is used, from −1 to 1/2, which proves usefulness of the auxetic materials.

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Section: Final Remarksmentioning

confidence: 99%

The emergence of auxetic material as a result of optimal isotropic design

Czarnecki

Wawruch

2015

Physica Status Solidi (b)

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“…Recently several studies devoted to the design of tall buildings have appeared. An example here is [23,24] where a tower building model and exemplary 3D solutions obtained using a software based on systems of structural frames described by Michell were presented.…”

Section: Application Of Algorithm To Analysis Of Tall Buildingsmentioning

confidence: 99%

Topology Optimization – a Variational Formulation of the Problem and Example Application

Kutylowski

Szwechłowicz

2020

Period. Polytech. Civil Eng.

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A variational formulation of the topology optimization problem is presented. A strain energy functional, being an equivalent of compliance, was minimized while constraints were imposed on the body mass. A global mass constraint and a local constraint on the amount of mass accumulated in a single material point of the body were adopted. A penalization procedure was defined and implemented in the optimization process to speed up the latter. The procedure in the successive optimization process steps translocates mass within the design domain, from the less strained areas to the more strained ones. The optimization process was described as a series of sequences of topologies determined using various control parameters, including different threshold functions. This means that the optimization process is characterized by a sequence of objective functional values approaching a minimal value. Various functions updating Young’s modulus were considered. Primarily the updating method referred to as SIMP was adopted. Three ways of using the discrete strain energy value to update Young's modulus in the considered material point were taken into account. These were: the amount of energy accumulated in the preceding step, the sum of the amounts of energy from all the preceding steps and the average amount of energy from the last two steps. In order to ensure the global limiting condition a mass constancy satisfaction procedure was incorporated into the algorithm. The algorithm procedures are described in detail. Finally, the algorithm was used to analyze selected problem relating to the pavement structure and the structure of tall buildings.

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“…In the majority of designs, this approach has already been replaced by more accurate deterministic methods, among which the finite element method plays a crucial role, and they are largely implemented in commercial software. Such an optimization strategy is applied for example in [ 1 ]; its goal is commonly focused on structural topology [ 2 , 3 ]. The traditional deterministic design appears to be suboptimal when significant uncertainties must be taken into account, such as climatic loads, material uncertainties, assembly errors, and corrosion or soil conditions, just to name a few.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Reliability-Based Design Optimization Framework for the Steel Plate Girder with Corrugated Web Subjected to Corrosion

Sokołowski

Kamiński

2022

Materials

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This paper proposes the framework for reliability-based design optimization (RBDO) of structural elements with an example based on the corrugated web I-girder. It tackles the problem of topological optimization of corroding structures with uncertainties. Engineering restrictions follow a concept of the limit states (LS) and extend it for stability and eigenfrequency assessment. The reliability constraints include all the LS; they are computed according to first- and second-order reliability methods. The RBDO example minimizes the bridge girder cross-section while satisfying the structural reliability level for the ultimate and the serviceability limit states, stability, and eigenfrequency. It takes into consideration two uncorrelated random effects, i.e., manufacturing imperfection and corrosion. They are both Gaussian; the first of them is applied at assembly time, while the second is applied according to the time series. The example confronts three independent FEM models with an increasing level of detailing, and compares RBDO results for three concurrent probabilistic methods, i.e., the iterative stochastic perturbation technique (ISPT), the semi-analytical method, and the Monte Carlo simulation. This study proves that the RBDO analysis is feasible even for computationally demanding structures, can support automation of structural design, and that the level of detailing in the FEM models influences its results. Finally, it exemplifies that reliability restrictions for LS are much more rigorous than for their deterministic counterparts, and that the fastest ISPT method is sufficiently accurate for probabilistic calculations in this RBDO.

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Topology optimization in structural mechanics

Cited by 9 publications

References 85 publications

The emergence of auxetic material as a result of optimal isotropic design

The emergence of auxetic material as a result of optimal isotropic design

Topology Optimization – a Variational Formulation of the Problem and Example Application

Stochastic Reliability-Based Design Optimization Framework for the Steel Plate Girder with Corrugated Web Subjected to Corrosion

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