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Tauzowski P., Błachowski B., Logo J.♦, First-order reliability approach for fatigue resistant topology optimization of elastoplastic structures,
WCSMO, 14th World Congress of Structural and Multidisciplinary Optimization, 2021-06-13/06-18, Boulder, Colorado (US), No.207, pp.1-2, 2021 | |
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Tauzowski P., Błachowski B., Logo J.♦, First-order approach for structural topology optimization with low-cycle fatigue constraints,
LSCE, XXVII Conference of Lightweight Structures in Civil Engineering, 2021-12-02/12-03, Łódź (PL), pp.1-4, 2021Abstract: In the present study topology optimization with constraints on the probability of failure is presented. The proposed approach allows controlling the safety level during the optimization process. The number of cycles to structural failure in the case of low-cycle fatigue problem is chosen as a constraint. The low-cycle fatigue requires elastic-plastic formulation of the problem, because in the optimized structure the phenomenon related to accumulation of plastic deformation is observed. In order to estimate the probability of failure for this numerically complex problem, the First Order Reliability Method (FORM) is proposed. The above mentioned methodology is implemented in object-oriented code written in MATLAB programming language. Keywords: topology optimization, reliability analysis, low-cycle fatigue, object oriented programming Affiliations:
Tauzowski P. | - | IPPT PAN | Błachowski B. | - | IPPT PAN | Logo J. | - | other affiliation |
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Logo J.♦, Tauzowski P., Błachowski B., Topology optimization of elastoplastic structures under reliability constraints: A first order approach,
CIVIL-COMP-OPTI 2019, Fifth International Conference on Soft Computing & Optimisation in Civil, Structural and Environmental Engineering, 2019-09-16/09-19, Riva del Garda (IT), pp.1-3, 2019Abstract: Structural safety is a critical aspect in modern engineering practice. One of the factors leading to the risk of failure is the variability of design parameters. To be able to estimate the risk of failure, this variability should be taken into account in design process. One way to tackle this issue is to assume a random nature of selected design parameters. These parameters can represent: loads acting on a structure, material properties or shape parameters. Minimizing the structural mass in the process of topology optimization is equivalent to removing the material from the initial, usually regular design space. This process can lead also to a reduction of the structural safety. Therefore, apart from deterministic constraints (such as stresses, displacements or load capacity), it is also worth to control the probabilistic ones. The purpose of this work is to introduce in topology optimization of elastoplastic structures an additional constraint on the probability of failure. Deterministic constraints, in the form of constraints on stresses, are imposed on elastoplastic analysis and utilized by the return mapping algorithm. One of the difficulties coming from the application of these random effects in the process topology optimization is its numerical complexity. Topological optimization itself is a complex issue. Adding a structural safety estimation can extend this process significantly. Fortunately, in the field of reliability analysis, which deals with determining reliability, there are methods that allow for relatively fast estimation of the probability of failure. These are First and Second Order Reliability Methods (FORM, SORM). Only several finite element iterations are sufficient to determine the probability of failure. These methods are based on the concept of the design point or the most probable point. This is the point on the limit state surface that lies closest to the mean point, and represents the most probable failure scenario. Moreover, approximation of limit state surface is linear (FORM) or quadratic (SORM). This allows to estimate quite accurately low probabilities of failure. Such a low probability of failure should characterized a safe structure. The search for a design point is based on the iterative formula developed by Rackwitz and Fiesler. The paper will present the formulation of the elasto-plastic problem of structural analysis as well as the detailed description of the algorithm for topology optimization under reliability constraint. The paper will be illustrated by examples, in which we will demonstrate, how probability of failure changes in the topological optimization process. Keywords: topology optimization, elasto-plastic structures, reliability analysis, probabilistic design Affiliations:
Logo J. | - | other affiliation | Tauzowski P. | - | IPPT PAN | Błachowski B. | - | IPPT PAN |
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Tauzowski P., Błachowski B., Logo J.♦, Stress constrained structural topology optimization with functor-oriented finite element implementation,
Workshop on Semidefinite Programming: Theory and Applications, 2018-10-19/10-19, Edinburgh (GB), pp.1, 2018Abstract: Classical programming of finite elements contains usual class, which duty is not only to approximate some physical field of interest (displacements, accelerations or temperature), but also definition of matrices necessary for particular analysis. It often leads to sophisticated class hierarchy of finite elements. In our approach matrices necessary for FE analysis are in separate classes. Hierarchy of these classes can be developed almost separately from declaration of the finite element class. Also finite elements hierarchy is much smaller, because each class represents one kind of matrix computed in FE analysis. In our opinion the functor is best suited object for this kind of approach. The functor represents one subroutine and it can also be invoked as function. The study presents application of functor oriented programming to finite element analysis. Keywords: stress constrained topology optimization, finite element programming, functor-oriented implemenetation Affiliations:
Tauzowski P. | - | IPPT PAN | Błachowski B. | - | IPPT PAN | Logo J. | - | other affiliation |
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