Local stress constraints in topology optimization of structures subjected to arbitrary dynamic loads: a stress aggregation-free approach

2021 ◽  
Author(s):  
Oliver Giraldo-Londoño ◽  
Miguel A. Aguiló ◽  
Glaucio H. Paulino
Keyword(s):  
Topology Optimization ◽  
Local Stress ◽  
Stress Constraints ◽  
Dynamic Loads

Topology optimization with local stress constraints: a stress aggregation-free approach

2020 ◽  
Vol 62 (4) ◽  
pp. 1639-1668
Author(s):  
Fernando V. Senhora ◽  
Oliver Giraldo-Londoño ◽  
Ivan F. M. Menezes ◽  
Glaucio H. Paulino
Keyword(s):  
Topology Optimization ◽  
Local Stress ◽  
Stress Constraints

TOPOLOGY OPTIMIZATION OF STRUCTURE WITH GLOBAL STRESS CONSTRAINTS BY INDEPENDENT CONTINUUM MAP METHOD

2006 ◽  
Vol 03 (03) ◽  
pp. 295-319 ◽  
Author(s):  
Y. K. SUI ◽  
X. R. PENG ◽  
J. L. FENG ◽  
H. L. YE
Keyword(s):  
Topology Optimization ◽  
Optimization Model ◽  
Strain Energy ◽  
Local Stress ◽  
Stress Constraints ◽  
Weighting Coefficient ◽  
Load Case ◽  
Weighting Method ◽  
Global Strain ◽  
Energy Constraints

We establish topology optimization model in terms of Independent Continuum Map method (ICM), so as to avoid the difficulties caused by multiple objective functions of compliance, owing to referring to weight as objective function. Using the distorted-strain-energy criterion, we transform stress constraints on all elements into structure strain-energy constraints in global sense. Then, the problem of topological optimum of continuum structure subjected to global strain-energy constraints is formulated and solved. The process of optimization is conducted through three basic steps which include the computation of the minimum strain energy of structure corresponding to the maximum strain-energy under the load case due to prescribing weight constraint, the determination of the allowable strain-energy of structure for every load case by using a formula from our numerical tests, as well as the establishment and solution of optimization model with the weight function due to all allowable strain energies. A strategy that is available to cope with complicated load ill-posedness in terms of different complementary approaches one by one is presented in the present work. Several numerical examples demonstrate that the topology path of transferring forces can be obtained more readily by global strain energy constraints rather than local stress constraints, and the problem of load ill-posedness can be tackled very well by the weighting method with regard to structural strain energy as weighting coefficient.

scholarly journals Damage approach: A new method for topology optimization with local stress constraints

2015 ◽  
Vol 53 (5) ◽  
pp. 1081-1098 ◽  
Author(s):  
Alexander Verbart ◽  
Matthijs Langelaar ◽  
Fred van Keulen
Keyword(s):  
Topology Optimization ◽  
Local Stress ◽  
Stress Constraints ◽  
New Method

scholarly journals A unified approach for topology optimization with local stress constraints considering various failure criteria: von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler– Pister and Willam–Warnke

2020 ◽  
Vol 476 (2238) ◽  
pp. 20190861 ◽  
Author(s):  
Oliver Giraldo-Londoño ◽  
Glaucio H. Paulino
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Local Stress ◽  
Stress Constraints ◽  
Failure Criteria ◽  
Yield Function ◽  
Material Failure ◽  
Local Material ◽  
Gradient Based ◽  
Von Mises

An interesting, yet challenging problem in topology optimization consists of finding the lightest structure that is able to withstand a given set of applied loads without experiencing local material failure. Most studies consider material failure via the von Mises criterion, which is designed for ductile materials. To extend the range of applications to structures made of a variety of different materials, we introduce a unified yield function that is able to represent several classical failure criteria including von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler–Pister and Willam–Warnke, and use it to solve topology optimization problems with local stress constraints. The unified yield function not only represents the classical criteria, but also provides a smooth representation of the Tresca and the Mohr–Coulomb criteria—an attribute that is desired when using gradient-based optimization algorithms. The present framework has been built so that it can be extended to failure criteria other than the ones addressed in this investigation. We present numerical examples to illustrate how the unified yield function can be used to obtain different designs, under prescribed loading or design-dependent loading (e.g. self-weight), depending on the chosen failure criterion.

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