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 with Stress Constraints: Reduction of Stress Concentration in Functionally Graded Structures

2008 ◽  
Author(s):  
Fernando V. Stump ◽  
Emílio C. N. Silva ◽  
Glaucio H. Paulino ◽  
Glaucio H. Paulino ◽  
Marek-Jerzy Pindera ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Stress Concentration ◽  
Stress Constraints ◽  
Functionally Graded ◽  
Graded Structures ◽  
Functionally Graded Structures

scholarly journals DESCRIBING STRESS CONCENTRATION FACTORS OF AN INTERNALLY PRESSURIZED CYLINDER WITH AN IMBEDDED HOLE BY NEW FORMULATION

2020 ◽  
Author(s):  
javad jafari fesharaki
Keyword(s):  
Stress Concentration ◽  
Three Dimensional ◽  
Fe Analysis ◽  
Internal Diameter ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
New Formulation ◽  
Von Mises ◽  
Von Mises Stresses ◽  
Pressurized Cylinder

The purpose of this paper is to investigate the stress concentration factor(SCF) for an internallypressurized cylinder with hole and based on detailed three-dimensional elastic FE analysis, a newcomprehensive set of formulas for SCFs are proposed. These stress concentration factors are presentedand discussed as a function of the ratio of cylinder diameter to the thickness of cylinder and hole diameter.The first ratio “D/100t” is equal to 1, 1.25, 1.5, 1.75, 2, 2.5, 2.75, 3, 3.25 and 3.5 and the second ratio“D/10d”, cylinder internal diameter to the hole diameter, varies from 0.6, 0.9, 1.2, 1.5, 1.8, 2, 2.3, 2.7,3.1and 3.5. Results are also presented for SCF of longitudinal, circumferential and Von Mises stresses.

scholarly journals The sensitivity of contact stresses in the mandibular premolar region to the shape of Zirconia dental implant: A 3D finite element study

2018 ◽  
Vol 24 (2) ◽  
pp. 55-63 ◽  
Author(s):  
Duraisamy Velmurugan ◽  
Masilamany Santha Alphin ◽  
Benedict Jain AR Tony
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cortical Bone ◽  
Transition Region ◽  
Dental Implant ◽  
Cancellous Bone ◽  
Contact Stresses ◽  
Thread Profile ◽  
Von Mises ◽  
Von Mises Stresses

Abstract Background: Implant thread profile plays a vital role in magnitude and distribution of contact stresses at the implant-bone interface. The main goal of this study was to evaluate the biomechanical effects of four distinct thread profiles of a dental implant in the mandibular premolar region. Methods: The dental implant represented the biocompatible Zirconia material and the bone block was modelled as transversely isotropic and elastic material. Three-dimensional finite element simulations were conducted for four distinct thread profiles of a dental implant at 50%, 75%, and 100% osseointegration. An axial static load of 500 N was applied on the abutment surface to estimate the stresses acting within the bones surrounding the implant. Results: Regions of stress concentration were seen mostly along the mesiodistal direction compared to that in the buccolingual direction. The cortical bone close to the cervical region of the implant and the cortical bone next to the first thread of the implant experienced peak stress concentration. Increasing the degree of osseointegration resulted in increased von-Mises stresses on the implant-cortical transition region, the implant-cancellous transition region, the cortical bone, and the cancellous bone. Conclusion: The results show that the application of distinct thread profiles at different degrees of osseointegration had significant effect on the stresses distribution contours in the surrounding bony structure. Comparing all four thread profiles, a dental implant with V-thread profile induced lower values of von-Mises stresses and shear stresses on the implant-cortical transition region, implant-cancellous transition region, cortical bone, and cancellous bone.

scholarly journals Influence of sagittal root positions on the stress distribution around custom-made root-analogue implants: a three-dimensional finite element analysis

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Chunping Lin ◽  
Hongcheng Hu ◽  
Junxin Zhu ◽  
Yuwei Wu ◽  
Qiguo Rong ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stress Concentration ◽  
Class I ◽  
Von Mises Stress ◽  
Element Analysis ◽  
Custom Made ◽  
Root Position ◽  
Von Mises ◽  
Von Mises Stresses

Abstract Background Stress concentration may cause bone resorption even lead to the failure of implantation. This study was designed to investigate whether a certain sagittal root position could cause stress concentration around maxillary anterior custom-made root-analogue implants via three-dimensional finite element analysis. Methods The von Mises stresses in the bone around implants in different groups were compared by finite element analysis. Six models were constructed and divided into two groups through Geomagic Studio 2012 software. The smooth group included models of unthreaded custom-made implants in Class I, II or III sagittal root positions. The threaded group included models of reverse buttress-threaded implants in the three positions. The von Mises stress distributions and the range of the stresses under vertical and oblique loads of 100 N were analyzed through ANSYS 16.0 software. Results Stress concentrations around the labial lamella area were more prominent in the Class I position than in the Class II and Class III positions under oblique loading. Under vertical loading, the most obvious stress concentration areas were the labial lamella and palatal apical areas in the Class I and Class III positions, respectively. Stress was relatively distributed in the labial and palatal lamellae in the Class II position. The maximum von Mises stresses in the bone around the custom-made root-analogue implants in this study were lower than around traditional implants reported in the literature. The maximum von Mises stresses in this study were all less than 25 MPa in cortical bone and less than 6 MPa in cancellous bone. Additionally, compared to the smooth group, the threaded group showed lower von Mises stress concentration in the bone around the implants. Conclusions The sagittal root position affected the von Mises stress distribution around custom-made root-analogue implants. There was no certain sagittal root position that could cause excessive stress concentration around the custom-made root-analogue implants. Among the three sagittal root positions, the Class II position would be the most appropriate site for custom-made root-analogue implants.

scholarly journals On the Topology Optimization of Elastic Supporting Structures under Thermomechanical Loads

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Jie Hou ◽  
Ji-Hong Zhu ◽  
Qing Li
Keyword(s):  
Topology Optimization ◽  
Adjoint Method ◽  
Stress Constraints ◽  
Optimized Design ◽  
Elastic Supports ◽  
Domain Optimization ◽  
Stress Measure ◽  
Optimization Formulation ◽  
Global Stress ◽  
Supporting Structures

This paper is to present a thermomechanical topology optimization formulation. By designing structures that support specific nondesignable domain, optimization is to suppress the stress level in the nondesignable domain and maintain global stiffness simultaneously. A global stress measure based onp-norm function is then utilized to reduce the number of stress constraints in topology optimization. Sensitivity analysis employs adjoint method to derive the global stress measure with respect to the topological pseudodensity variables. Some particular behaviors in thermomechanical topology optimization of elastic supports, such as the influence of different thermomechanical loads and the existence of intermediate material, are also analyzed numerically. Finally, examples of elastic supports on a cantilever beam and a nozzle flap under different thermomechanical loads are tested with reasonable optimized design obtained.

Conceptual Design of Structures Using an Upper Bound of von Mises Stress

2018 ◽  
Vol 19 (1) ◽  
Author(s):  
Ashok V. Kumar
Keyword(s):  
Topology Optimization ◽  
Stress Concentration ◽  
Upper Bound ◽  
Von Mises Stress ◽  
Optimization Approach ◽  
Objective Functions ◽  
Stress Concentrations ◽  
Handling Stress ◽  
Design Concepts ◽  
Von Mises

Optimal layouts for structural design have been generated using topology optimization approach with a wide variety of objectives and constraints. Minimization of compliance is the most common objective but the resultant structures often have stress concentrations. Two new objective functions, constructed using an upper bound of von Mises stress, are presented here for computing design concepts that avoid stress concentration. The first objective function can be used to minimize mass while ensuring that the design is conservative and avoids stress concentrations. The second objective can be used to tradeoff between maximizing stiffness versus minimizing the maximum stress to avoid stress concentration. The use of the upper bound of von Mises stress is shown to avoid singularity problems associated with stress-based topology optimization. A penalty approach is used for eliminating stress concentration and stress limit violations which ensures conservative designs while avoiding the need for special algorithms for handling stress localization. In this work, shape and topology are represented using a density function with the density interpolated piecewise over the elements to obtain a continuous density field. A few widely used examples are utilized to study these objective functions.

Topology Optimization of Structures Using a Global Stress Measure

2012 ◽  
Author(s):  
Vijay Krishna Yalamanchili ◽  
Ashok V. Kumar
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Continuous Distribution ◽  
Stress Constraints ◽  
Von Mises Stress ◽  
Feasible Region ◽  
Barrier Method ◽  
Stress Measure ◽  
Global Stress ◽  
Mean Compliance

An approach for stress based topology optimization is studied here where stress constraints for continuum structures are imposed using a conservative global stress measure. A relation between the mean compliance and Von-Mises stress is used to construct an objective function that minimizes mass until stress constraints are activated. This approach is implemented in a mesh independent finite element framework where the feasible region is defined using boundary equations while analysis and topology optimization are performed on a background mesh. The SIMP approach is used for topology optimization and nodal values of density are treated as the design variables. The density field is interpolated over the elements to obtain a continuous distribution. To ensure smooth boundaries a smoothing term is also added to the objective function which minimizes gradient of the density function. The optimization problem is then solved using Moving Barrier Method (MBM). Several examples are studied to evaluate this approach.

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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