Stress-based topology optimization

Yang, Ren‐Jye; Chen, C. J.

doi:10.1007/bf01196941

Cited by 306 publications

(137 citation statements)

References 13 publications

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“…This has been done in a somewhat similar way before in [31], [20] and [14], but our modification is different as will be discussed below. The P-norm stress measure for cluster…”

Section: Stress Measurementioning

confidence: 99%

Stress constrained topology optimization

Holmberg

Torstenfelt

Klarbring

2013

Struct Multidisc Optim

324

167

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This paper develops and evaluates a method for handling stress constraints in topology optimization. The stress constraints are used together with an objective function that minimizes mass or maximizes stiffness, and in addition, the traditional stiffness based formulation is discussed for comparison. We use a clustering technique, where stresses for several stress evaluation points are clustered into groups using a modified P-norm to decrease the number of stress constraints and thus the computational cost. We give a detailed description of the formulations and the sensitivity analysis. This is done in a general manner, so that different element types and 2D as well as 3D structures can be treated. However, we restrict the numerical examples to 2D structures with bilinear quadrilateral elements.The three formulations and different approaches to stress constraints are compared using two well known test examples in topology optimization: the L-shaped beam and the MBB-beam. In contrast to some other papers on stress constrained topology optimization, we find that our formulation gives topologies that are significantly different from traditionally optimized designs, in that it actually manage to avoid stress concentrations. It can therefore be used to generate conceptual designs for industrial applications.

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“…This has been done in a somewhat similar way before in [31], [20] and [14], but our modification is different as will be discussed below. The P-norm stress measure for cluster…”

Section: Stress Measurementioning

confidence: 99%

Stress constrained topology optimization

Holmberg

Torstenfelt

Klarbring

2013

Struct Multidisc Optim

324

167

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“…The implant domain is within the boundary domain of the lower modulus of elasticity (bone). This boundary domain will eliminate the need to extract a design model for certain applications as it is being done within the conventional topology optimization design process [35] [36] [37]. The design takes into consideration the original state of the finite element analysis of the mandible.…”

Section: Numerical Examplesmentioning

confidence: 99%

Topology Optimization and Fatigue Analysis of Temporomandibular Joint Prosthesis

Al-Ali¹,

Al-Ali²,

Takezawa³

et al. 2017

WJM

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Treatment of bone tumors in the mandible often involves extensive excavation of affected bone, followed by mandibular reconstruction. Prosthetic implants may be needed to restore jaw functionality. The challenges of making prosthetic bone implants include stress shielding and extending the mechanical life of the implant. We have developed a design algorithm to improve the efficiency of prosthesis design. A finite element model of the patient case is constructed from a computer tomography scan, and the computer implements topology optimization techniques to design the prosthesis with limited stress shielding affected by highly biomechanical compatibility. Topology optimization facilitates the design of low weight structures by automatically introducing holes into the structure. This is governed by engineering predetermined constraints to meet certain job specifications. Such a design will be tested for fatigue life before it is ready to be manufactured and used. Topology optimization can be performed as a design process to achieve a final design that takes stress shielding into consideration. The problem of stress shielding is solved by matching the stiffness of the orthopedic implant to the original bone that is being replaced. The material we used was titanium alloy (Ti-6Al-7Nb). Volume fraction of the orthodox implant was used (0.2872 for the studied case) as volume constraints. Compliance of the bulk bone was set as a further constraint to match the stiffness of the bone with the designed structure. Our results show a good life expectancy for the designed parts, with 12% higher life expectancy for stress-based topology optimization than for compliance-based topology optimization.

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“…It has been shown that the crucial point was the computational effort to solve the optimization problem. A global stress approach, using aggregation of the local constraints techniques either based on the p-norm, the p-mean or the Kresselmeier Steinhauser (KS) function were proposed by Duysinx and Sigmund (1998) and Yang and Chen (1996) to overcome the issue related to the previous local approach. It was shown the the global CPU time was effectively reduced, but the robustness of a local control was generally lost.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization for minimum weight with compliance and simplified nominal stress constraints for fatigue resistance

Collet

Bruggi

Duysinx

2016

Struct Multidisc Optim

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This work investigates a simplified approach to cope with the optimization of preliminary design of structures under local fatigue constraints along with a global enforcement on the overall compliance. The problem aims at the minimization of the weight of linear elastic structures under given loads and boundary conditions. The expected stiffness of the optimal structure is provided by the global constraint, whereas a set of local stress-based constraints ask for a structure to be fatigue resistant. A modified Goodman fatigue strength comparison is implemented through the same formalism to address pressure-dependent failure in materials as in Drucker-Prager strength criterion. As a simplification, the Sines approach is used to define the equivalent mean and alternating stresses to address the fatigue resistance for an infinite life time. Sines computation is based on the equivalent mean and alternate stress depending on the invariants of the stress tensor and its deviatoric

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Stress-based topology optimization

Cited by 306 publications

References 13 publications

Stress constrained topology optimization

Stress constrained topology optimization

Topology Optimization and Fatigue Analysis of Temporomandibular Joint Prosthesis

Topology optimization for minimum weight with compliance and simplified nominal stress constraints for fatigue resistance

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