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.

Finding Better Local Optima in Topology Optimization via Tunneling

2018 ◽  
Author(s):  
Shanglong Zhang ◽  
Julián A. Norato
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Structural Response ◽  
Free Form ◽  
Local Optima ◽  
Design Representation ◽  
Tunneling Method ◽  
Optimization Parameters ◽  
Gradient Based ◽  
Geometric Primitives

Topology optimization problems are typically non-convex, and as such, multiple local minima exist. Depending on the initial design, the type of optimization algorithm and the optimization parameters, gradient-based optimizers converge to one of those minima. Unfortunately, these minima can be highly suboptimal, particularly when the structural response is very non-linear or when multiple constraints are present. This issue is more pronounced in the topology optimization of geometric primitives, because the design representation is more compact and restricted than in free-form topology optimization. In this paper, we investigate the use of tunneling in topology optimization to move from a poor local minimum to a better one. The tunneling method used in this work is a gradient-based deterministic method that finds a better minimum than the previous one in a sequential manner. We demonstrate this approach via numerical examples and show that the coupling of the tunneling method with topology optimization leads to better designs.

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

Non-Probabilistic Based Topology Optimization Under External Load Uncertainty With Eigenvalue-Superposition of Convex Models

2013 ◽  
Author(s):  
Xike Zhao ◽  
Hae Chang Gea ◽  
Wei Song
Keyword(s):  
Topology Optimization ◽  
External Load ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Convex Model ◽  
Structure Response ◽  
Gradient Based ◽  
Bounded Convex ◽  
Topology Optimization Method

In this paper the Eigenvalue-Superposition of Convex Models (ESCM) based topology optimization method for solving topology optimization problems under external load uncertainties is presented. The load uncertainties are formulated using the non-probabilistic based unknown-but-bounded convex model. The sensitivities are derived and the problem is solved using gradient based algorithm. The proposed ESCM based method yields the material distribution which would optimize the worst structure response under the uncertain loads. Comparing to the deterministic based topology optimization formulation the ESCM based method provided more reasonable solutions when load uncertainties were involved. The simplicity, efficiency and versatility of the proposed ESCM based topology optimization method can be considered as a supplement to the sophisticated reliability based topology optimization methods.

Response, Localization, and Rupture of Anisotropic Tubes Under Combined Pressure and Tension

2020 ◽  
Vol 88 (1) ◽  
Author(s):  
Martin Scales ◽  
Kelin Chen ◽  
Stelios Kyriakides
Keyword(s):  
Constitutive Model ◽  
Ductile Failure ◽  
Failure Criteria ◽  
Yield Function ◽  
Local Deformation ◽  
Al Alloys ◽  
Biaxial Stress ◽  
Image Correlation ◽  
Element Analysis ◽  
Von Mises

Abstract The inelastic response and failure of Al-6061-T6 tubes under combined internal pressure and tension is investigated as part of a broader study of ductile failure of Al-alloys. A custom experimental setup is used to load thin-walled tubes to failure under radial paths in the axial-hoop stress space. All loading paths achieve nominal stress maxima beyond which deformation localizes into a narrow band. 3D digital image correlation (DIC) was used to monitor the deformations in the test section and successfully captured the rapid growth of strain within the localization bands where they burst. The biaxial stress states generated are first used to calibrate the nonquadratic anisotropic Yld04-3D yield function (Barlat et al., 2005, “Linear Transformation-based Anisotropic Yield Functions,” Int. J. Plasticity, 21(5), pp. 1009–1039). The constitutive model is then incorporated through a UMAT into a finite element analysis and used to simulate numerically the experiments. The same calculations were performed using von Mises (VM) and an isotropic nonquadratic yield function. The material hardening responses adopted were extracted for each constitutive model from the necked zone of a tensile test using an inverse method. The use of solid elements captures the evolution of local deformation deep into the localizing part of the response, producing strain levels that are required in the application of failure criteria. The results demonstrate that the adoption of a nonquadratic yield function, together with a correct material hardening response are essential for large deformation predictions in localizing zones in Al-alloys. Including the anisotropy in such a constitutive model produces results that are closest to the experiments.

Application of the Deformation Theory of Plasticity for Determining Elastoplastic Stress and Strain Concentration Factors

1976 ◽  
Vol 98 (4) ◽  
pp. 1152-1156 ◽  
Author(s):  
J. P. Eimermacher ◽  
I.-Chih Wang ◽  
M. L. Brown
Keyword(s):  
Deformation Theory ◽  
Analytical Data ◽  
Local Stress ◽  
Failure Criteria ◽  
Constitutive Law ◽  
Stress And Strain ◽  
Strain Concentration ◽  
Theory Of Plasticity ◽  
Concentration Factors ◽  
Von Mises

The deformation theory of plasticity is considered as a means for obtaining a solution to the problem of calculating stress and strain concentration factors at geometric discontinuities where the local stress state exceeds the yield strength of the material. Through the use of the Hencky-Nadai constitutive law and the Von Mises failure criteria, the elastoplastic element stiffness matrix is derived for a plane stress triangular plate element. An elastoplastic solution is arrived at by considering direct-iterative and finite element techniques. Verification of the analytical results is obtained by considering a numerical example and comparing the calculated results with published experimental and analytical data.

Design of flexure hinges based on stress-constrained topology optimization

2016 ◽  
Vol 231 (24) ◽  
pp. 4635-4645 ◽  
Author(s):  
Min Liu ◽  
Xianmin Zhang ◽  
Sergej Fatikow
Keyword(s):  
Topology Optimization ◽  
Stress Concentration ◽  
Stress Constraints ◽  
Stress Constraint ◽  
Flexure Hinges ◽  
Weighted Sum Method ◽  
Stress Measure ◽  
Von Mises ◽  
Von Mises Stresses ◽  
Sharp Corners

Stress concentration is one of the disadvantages of flexure hinges. It limits the range of motion and reduces the fatigue life of mechanisms. This article designs flexure hinges by using stress-constrained topology optimization. A weighted-sum method is used for converting the multi-objective topology optimization of flexure hinges into a single-objective problem. The objective function is presented by considering the compliance factors of flexure hinges in the desired and other directions. The stress constraint and other constraint conditions are developed. An adaptive normalization of the P-norm of the effective von Mises stresses is adopted to approximate the maximum stress, and a global stress measure is used to control the stress level of flexure hinges. Several numerical examples are performed to indicate the validity of the method. The stress levels of flexure hinges without and with stress constraints are compared. In addition, the effects of mesh refinement and output spring stiffness on the topology results are investigated. The stress constraint effectively eliminates the sharp corners and reduces the stress concentration.

Topology optimization of structures subject to self-weight loading under stress constraints

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Renatha Batista dos Santos ◽  
Cinthia Gomes Lopes
Keyword(s):  
Topology Optimization ◽  
Stress Constraints ◽  
Topological Derivative ◽  
The Self ◽  
Von Mises Stress ◽  
Stress Constraint ◽  
Content Type ◽  
Derivative Method ◽  
Von Mises ◽  
Weight Loading

PurposeThe purpose of this paper is to present an approach for structural weight minimization under von Mises stress constraints and self-weight loading based on the topological derivative method. Although self-weight loading topology has been the subject of intense research, mainly compliance minimization has been addressed.Design/methodology/approachThe resulting minimization problem is solved with the help of the topological derivative method, which allows the development of efficient and robust topology optimization algorithms. Then, the derived result is used together with a level-set domain representation method to devise a topology design algorithm.FindingsNumerical examples are presented, showing the effectiveness of the proposed approach in solving a structural topology optimization problem under self-weight loading and stress constraint. When the self-weight loading is dominant, the presence of the regularizing term in the formulation is crucial for the design process.Originality/valueThe novelty of this research work lies in the use of a regularized formulation to deal with the presence of the self-weight loading combined with a penalization function to treat the von Mises stress constraint.

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.

Buckling Topology Optimization of Laminated Multi-Material Composite Structures

2006 ◽  
Author(s):  
Erik Lund
Keyword(s):  
Topology Optimization ◽  
Composite Structures ◽  
Optimization Problems ◽  
Combinatorial Problem ◽  
Optimization Method ◽  
Load Factor ◽  
Material Optimization ◽  
Material Stiffness ◽  
Gradient Based ◽  
Material Composite

The design problem of maximizing the buckling load factor of laminated multi-material composite shell structures is investigated using the so-called Discrete Material Optimization (DMO) approach. The design optimization method is based on ideas from multi-phase topology optimization where the material stiffness is computed as a weighted sum of candidate materials, thus making it possible to solve discrete optimization problems using gradient based techniques and mathematical programming. The potential of the DMO method to solve the combinatorial problem of proper choice of material and fiber orientation simultaneously is illustrated for a multilayered plate example and a simplified shell model of a spar cap of a wind turbine blade.

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