Global Stress Measure Research Articles

An improved evolutionary structure optimization method considering stress minimization and smooth design

AbstractThe design of continuum structures often presents challenges related to stress concentration, which can cause significant structural damage. To address this issue, the current study presents a new stress minimization method that utilizes the Windowed Evolutionary Structural Optimization (WESO) framework. The method aims to improve algorithm stability by optimizing design variables with an intermediate density. The use of a P‐norm stress aggregation method improves the assessment of global stress levels and enhances computational efficiency. Furthermore, a stable element sensitivity formulation, derived from the adjoint sensitivity analysis of the global stress measure, effectively handles the nonlinear stress behavior. Mesh filtering techniques are utilized to convert sensitivity from elements to nodes, and the structural topological solution is represented using the level set function (LSF) based on element‐node sensitivity. This method addresses the singularity issue commonly found in density‐based optimization methods and facilitates the achievement of smooth topological solutions. Through 2D and 3D benchmark designs, the proposed method's feasibility, stability, and superiority are thoroughly demonstrated. A parametric study is conducted to identify the optimal parameter range for the algorithm, leading to the development of a rational method for parameter selection. The optimized topology, with its smooth boundaries, can guide the design of structures without the need for redesign or post‐processing, helping to drive innovation and development in engineering.

Beyond Role Conflict and Ambiguity: A Global Measure of Role Stress among South African School Teachers

Background. Role stress is linked to reduced work performance, diminished organizational commitment, increased intention to leave a job, and negative physical and mental health effects. Given the significant implications of role stress, researchers have sought to understand and quantify the concept. The Role Conflict and Ambiguity (RCA) scales are widely utilized in job stress research as the predominant measurement tools. They were originally conceptualized as consisting of two independent dimensions: role conflict and role ambiguity. Objective. This study advances the validation research of the RCA scales by exploring its dimensionality through Mokken Scale Analysis (MSA) and Classical Test Theory (CTT). Method. South African school teachers responded to the RCA scales, Maslach Burnout Inventory, and Teaching Satisfaction Scale. Confirmatory Factor Analysis (CFA) and MSA were employed for data analysis. Results. The research determined that a second-order model provided the optimal fit, indicating that role ambiguity and role conflict are subordinate dimensions within the overarching construct of role stress. Conclusion. The findings from the CFA and supplementary bifactor indices reinforce the view that the instrument comprises 13 items, which assess a general dimension of role stress along with two sub-dimensions: role conflict and role ambiguity. Such specificity may lead to more effective strategies to mitigate role-related stress, thereby enhancing overall employee well-being, job satisfaction, and organizational productivity.

Stress-related topology optimization with multilevel smoothed isogeometric densities and Bézier elements

Isogeometric analysis (IGA) provides a feasible technique to seamlessly integrate computer-aided design (CAD) into the existing finite element analysis. In this article, a Bézier elements-based IGA method is established to address the stress-related topology optimization of structures, which incorporates geometrical representation, structural analysis and topology optimization into a unified process as well as can naturally handle the curvilinear edge elements for the stress problems. To enhance the smoothness of the structural boundaries, a multilevel isogeometric density field (IDF) defined at control points (CPs) is designed by utilizing the values of the non-uniform rational B-splines (NURBS) basis functions from the previous design iteration. A global stress measure is approximated by a smooth maximum function with an additional error term. The k-means clustering originally from signal processing is used to partition the stress observations with dynamic centroids and indices, which improves the accuracy of the sensitivity results. The sensitivity analyses of the stress-related problems are derived from the multilevel IDF model. Three kinds of numerical results are provided to illustrate the effectiveness of the proposed method to solve stress-related problems via the multilevel IDF model for achieving the optimal solution with smooth boundaries.

Stress constrained topology optimization of energy storage flywheels using a specific energy formulation

A variable density, stress-constrained topology optimization approach is used, along with the solid isotropic material with penalization (SIMP) power law and a P-norm aggregated global stress measure to optimize the rotor of a flywheel energy storage systems (FESS). A new specific energy maximization optimization formulation is proposed which eliminates the need to impose an arbitrary volume fraction constraint to the optimization problem as it is done in traditional kinetic energy maximization approaches. The FESS rotors obtained with the specific energy formulation achieved a 15.8% increase in the specific energy compared to the kinetic energy based approach which improved the specific energy by 12.8%. Factors such as the operating speed, maximum stress, rotational symmetry and rotor material also influence the moment of inertia and stress distribution in the flywheel, and the effects of these parameters on the optimal topology and its energy capacity are investigated. At low speeds, the topology is seen to have elongated holes, which become rounded and move away from central shaft as the speed is increased. The reverse effect is seen when the upper limit on the stress constraint is increased. While the choice of rotor material affects the kinetic energy and mass of the flywheel, its optimal topology and specific energy is seen to be nearly identical for rotor materials with the same Eρ ratio, and slightly different for other cases. The size of the circular sections used as the topology design domain is seen to affect the number of spokes in the rotor, but the overall specific energy is unaffected, so manufacturing considerations can be used to choose the rotational symmetry of the rotor. Due to the frequent charge–discharge cycles associated with short term storage, both centrifugal and acceleration forces might play an important role in determining the peak stresses in the flywheel. Therefore, the influence of acceleration loads on the optimal rotor topology is also studied and shown to only have an impact for very large instantaneous accelerations of 5235.9 rad/s2 or higher.

Reliability-based topology optimization using the response surface method for stress-constrained problems considering load uncertainty

The objective of this work is to build a useful-response-surface-based reliability design approach for solving stress-constrained optimization problems taking into consideration load uncertainty. To this end, a reliability optimization problem of minimizing the volume fraction while satisfying a global probabilistic stress constraint is formulated, in which a Kreisselmeier–Steinhauser-function-based aggregate approach with a correction parameter is introduced to ensure accurate approximation of the maximum stress. To avoid the expensive computational cost of calculating the sensitivity of the global maximum stress with respect to random loads in reliability evaluation, a response-surface-based global stress measure is established. Finally, several typical design instances are solved to prove the performance of the presented methodology. The importance of considering load uncertainty in stress-related topology optimization is also explained by comparing the results acquired by the presented reliability-based topology optimization methodology with deterministic designs.

Stress-based topology optimization of continuum structures under harmonic force excitation

In this paper, a new optimization method for the maximum von Mises stress minimization design of continuum structures subjected to harmonic force excitation is proposed. By using an extended Bi-directional Evolutionary Structural Optimization (BESO) method, the intermediate density elements with high stress state are avoided. To reduce the computational cost, the global von Mises stress is approximately measured by using a global stress measure based on the p-norm. Both sensitivities and topological variables are filtered to overcome the highly nonlinear stress behavior and stabilize the optimization procedure. A series of comparisons have been conducted to validate the effectiveness and practicability of the method on two-dimensional and three-dimensional benchmark design problems. The influence of varying excitation frequencies, damping and boundary conditions on the optimized results and the mode shapes are considered. The optimized results indicate that the proposed approach has good convergence and can achieve a reasonable design that effectively reduces the stress concentration effect at the critical stress areas. Strength of engineering structure under harmonic load is improved.

Level set-based topology optimization for compliance and stress minimization of shell structures using trimmed quadrilateral shell meshes

In this paper, a novel level set-based topology optimization method for shell structures is presented to minimize both compliance and stress under a volume constraint. During the optimization process, trimmed quadrilateral shell meshes are generated by cutting a background quadrilateral shell mesh with the zero-isolines of a level set function. Polygonal shell elements with assumed strains are used for the trimmed quadrilateral shell elements created along the boundaries of shell structures. A new sensitivity field for the evolution of a level set function is proposed to minimize both compliance and stress of shell structures. A p -norm function is employed to aggregate local stresses into a single global stress measure in the sensitivity analysis. Several numerical examples are carried out to show the validity and effectiveness of the proposed method.

An efficient 146-line 3D sensitivity analysis code of stress-based topology optimization written in MATLAB

This paper presents an efficient and compact MATLAB code for three-dimensional stress-based sensitivity analysis. The 146 lines code includes the finite element analysis and p-norm stress sensitivity analysis based on the adjoint method. The 3D sensitivity analysis for p-norm global stress measure is derived and explained in detail accompanied by corresponding MATLAB code. The correctness of the analytical sensitivity is verified by comparison with finite difference approximation. The nonlinear optimization solver is chosen as the Method of moving asymptotes (MMA). Three typical volume-constrained stress minimization problems are presented to verify the effectiveness of sensitivity analysis code. The MATLAB code presented in this paper can be extended to resolve different stress related 3D topology optimization problems. The complete program for sensitivity analysis is given in the Appendix and is intended for educational purposes. MATLAB code is additionally provided in electronic supplementary material for a simple cantilever beam optimization.

Thermo‐elastic topology optimization with stress and temperature constraints

AbstractA thermo‐elastic topology optimization with stress and temperature constraints is proposed to attack the complex multiphysics problem in this paper. Based on the rational approximation of material properties (RAMP), the coupled equations of mechanic and temperature field are solved. Two optimization problems, volume minimization with temperature and stress constraints, and traditional compliance minimization with volume and temperature constraints, are discussed for comparison. The stress stabilizing control scheme (SSCS) combined with global stress measure is presented to tackle highly nonlinear and local nature of stress with thermal expansion in varying temperature field. The adjoint method is applied to achieve the sensitivity of multiphysics field and the density function is updated utilizing the method of moving asymptotes (MMA). Representative examples are investigated to demonstrate the effectiveness and utility of the proposed method. Clear topology and stable iterative process can be obtained for complex coupled problem by means of the SSCS. Meanwhile, the topology with stress and temperature constraints has obvious sensitivity to even subtle change in temperature. The optimization design considering several stress constraints under multithermal conditions can work well in different temperature ranges.

Topology optimization of material nonlinear continuum structures under stress constraints

This paper proposes a methodology to extend the bi-directional evolutionary structural optimization (BESO) method for compliance minimization (stiffness maximization) design of material nonlinear continuum structures subject to both constraints on volume fraction and maximum von Mises stress. BESO method based on discrete variables can effectively avoid the well-known stress singularity problem in density-based methods with low density elements. The aggregated p-norm global stress measure is adopted to approximate the maximum von Mises stress. The conventional compliance design objective is augmented with p-norm stress measures by introducing one Lagrange multiplier. The Lagrange multiplier is employed to yield compromised designs of compliance and the p-norm stress. A scheme is developed for the determination of the Lagrange multiplier so that the maximum von Mises stress could be effectively constrained. The update of the binary topological design variables lies in the sensitivity numbers derived using the adjoint method. As for the highly nonlinear stress behavior, both topological variables and sensitivity numbers are filtered to stabilize the optimization procedure. The filtered sensitivity numbers are further stabilized with their historical information. A series of comparison studies has been conducted to validate the effectiveness of the method on several benchmark design problems.

Stress Relaxation and Sensitivity Weight for Bi-Directional Evolutionary Structural Optimization to Improve the Computational Efficiency and Stabilization on Stress-Based Topology Optimization

Stress-based topology optimization is one of the most concerns of structural optimization and receives much attention in a wide range of engineering designs. To solve the inherent issues of stress-based topology optimization, many schemes are added to the conventional bi-directional evolutionary structural optimization (BESO) method in the previous studies. However, these schemes degrade the generality of BESO and increase the computational cost. This study proposes an improved topology optimization method for the continuum structures considering stress minimization in the framework of the conventional BESO method. A global stress measure constructed by p-norm function is treated as the objective function. To stabilize the optimization process, both qp-relaxation and sensitivity weight scheme are introduced. Design variables are updated by the conventional BESO method. Several 2D and 3D examples are used to demonstrate the validity of the proposed method. The results show that the optimization process can be stabilized by qp-relaxation. The value of q and p are crucial to reasonable solutions. The proposed sensitivity weight scheme further stabilizes the optimization process and evenly distributes the stress field. The computational efficiency of the proposed method is higher than the previous methods because it keeps the generality of BESO and does not need additional schemes.

Personal resources and flexibility in coping with stress depending on perceived stress in a group of cancer patients

BackgroundCancer is a highly stressful life event. It requires the employment of new coping skills and strategies. Flexibility in coping with stress plays an important role in this case. The aim of the study was to assess the role of personal resources in shaping the flexi-bility in coping with stress among cancer patients depending on the level of perceived stress.Participants and procedureOne hundred eight patients suffering from cancer were surveyed. The following methods were employed: the Resiliency Meas-urement Scale by Ogińska-Bulik and Juczyński, the Adult Hope Scale by Snyder, the Spirituality Index of Well-Being by Daaleman and Frey, the Flexibility in Coping with Stress Questionnaire by Basińska and team and the Global Measure of Per-ceived Stress by Cohen, Kamarck and Mermelstein.ResultsThe results demonstrated a positive correlation between all considered personal resources and flexibility in coping. Both resiliency and spiritual well-being enable one to predict 23% of variability of flexibility in coping. Cluster analysis revealed that the group of patients with a generally higher level of personal resources was characterised by greater flexibility in all its dimensions. However, stress levels did not modify the relationships between personal resources and flexibility in coping.ConclusionsThe results encourage the planning of psychological interventions aimed at the development of personal resources among cancer patients, and warrant further research.

Multi-material structural topology optimization considering material interfacial stress constraints

For multi-material structures, ensuring material interface strength is particularly vital for their integrity and durability. In the present study, we incorporate material interfacial stress constraints into topology optimization of bi-material structures. A multi-material level set method, in conjunction with interface-conforming finite element meshes, is employed to describe the distribution of different material phases and to capture the evolution of the material interfaces. The use of interface-conforming meshes enables accurate analysis of both interfacial stresses and their design sensitivities. Noting that the interfacial strength failure is usually characterized by a tension/compression asymmetric mechanism, we adopt an equivalent interfacial stress (which was originally proposed for strength criterion concerning composite delamination) expressed by the interface tensile and tangential stresses in the considered strength criterion. To handle the local nature of such interfacial stress constraints, we propose a global stress measure, which is an approximation of the p-norm of the equivalent interfacial stress field. An adjoint sensitivity analysis scheme is derived by taking into account the interface transmission conditions. To treat multiple constraints (the volume constraints and the interfacial stress constraint) in level set-based topology optimization, the velocity field-level set method is employed. Numerical examples are presented to show effectiveness of the present method. It is also shown that the tension/compression asymmetric interfacial strength criteria may lead to asymmetric designs.

Uncertainty-oriented topology optimization of interval parametric structures with local stress and displacement reliability constraints

This paper presents the interval reliability-based topology optimization (IRBTO) framework and an effective solution procedure for interval parametric structures to achieve optimal material configurations under consideration of local stiffness and strength failure. Firstly, ε-relaxed stress criterion and global stress aggregation approach are involved to circumvent the stress singularity and multi-constrained problems. Combined the orthogonal polynomial expansion with the set allocation theorem, an interval dimension-by-dimension method (IDDM) is proposed to determine feasible bounds of structural responses under unknown-but-bounded load and material uncertainties. The interval reliability (IR) is then applied to handle the limited reliability constraints of concerned displacements and the global stress measure. Meanwhile, the adjoint-vector based sensitivity analysis of presented IR indexes to design variables is further discussed to avoid expensive computational cost from the large-scale nature of variable updating. The usage, rationality, and superiority of the developed methodology are demonstrated by several case applications.

Validation of oxidative stress assay for schizophrenia

Accumulating evidence implicates oxidative stress in a range of diseases, yet no objective measurement has emerged that characterizes the global nature of oxidative stress. Previously, we reported a measurement that employs the moderately strong oxidant iridium (Ir) to probe the oxidative damage in a serum sample and reported that in a small study (N = 15) the Ir-reducing capacity assay could distinguish schizophrenia from healthy control groups based on their levels of oxidative stress. Here, we used a larger sample size to evaluate the Ir-reducing capacity assay to assess its ability to discriminate the schizophrenia (N = 73) and healthy control groups (N = 45). Each serum sample was measured (in triplicate) at three different times that were separated by several weeks. The Intraclass Correlation Coefficient (ICC = 0.69) for these repeated measurements indicates the assay detects stable components in the sample (i.e., it is not detecting transient reactive species or air-oxidizable serum components). Correlations between the Ir-reducing capacity assay and independently-measured total serum protein levels (r = +0.74, p < 2.2 × 10−16) suggest the assay is detecting information in the protein pool. For cross-validation of the discrimination ability, we used machine learning and receiver operating characteristic (ROC) analysis. After adjusting for potential confounders (age and smoking status), an area under the curve (AUC) of ROC curve was calculated to be 0.89 (p = 9.3 × 10−5). In conclusion, this validation indicates the Ir-reducing capacity assay provides a simple global measure of oxidative stress, and further supports the hypothesis that oxidative stress is linked with schizophrenia.

Particle scale force sensor based on intensity gradient method in granular photoelastic experiments

The intensity gradient method (G2 method), namely computing the light intensity gradient-squared, is a widely used non-invasive experimental method to extract stress information from quasi-two-dimensional photoelastic granular materials. Previous works show that calibrated G2 is an accurate measure of global stress. However, whether it can be used at the particle scale aside from the special case of diametric loading remains unclear. We test here the applicability and limitations of G2 as particle scale stress indicator and specify its dependence on relevant experimental parameters of the particles, light conditions, and imaging system. We first propose an explicit formula to calculate the relationship between the G2 value and stress based on the linear elasticity and photoelasticity theories, and then validate our formula by numerical and experimental tests. We find that G2 is proportional to , the sum of magnitudes of the contact forces, for disc particles when forces are not large. We also observe that, for large enough resolution, G2 does not change with the number of contacts as well as the direction of the contact forces under same value. However, we find that this relation between G2 and is not universal for any particle shape. As an example, we show that a square particle can have dramatically different values of G2 under the same contact forces with different contact types (point-edge contact and edge–edge contact).

A level set–based method for stress‐constrained multimaterial topology optimization of minimizing a global measure of stress

SummaryIn multimaterial topology optimization of minimizing a global measure of stress, the maximum stresses in different materials may not satisfy the strength design requirements simultaneously if stress constraints for different materials are not considered. In this paper, a level set–based method is presented to handle the stress‐constrained multimaterial topology optimization of minimizing a global stress measure. Specifically, a multimaterial level set model is adopted to describe the structural topology, and a stress interpolation scheme is introduced for stress evaluation. Then, a stress penalty‐based topology optimization model is presented. Meanwhile, an adaptive adjusting scheme of the stress penalty factor is employed to improve the control of the local stress level. To solve the stress‐constrained multimaterial topology optimization problem minimizing the global measure of stress, the parametric level set method is employed, and the sensitivity analysis is carried out. Numerical examples are provided to demonstrate the effectiveness of the presented method. Results indicate that multimaterial structures with optimized global stress can be gained, and stress constraints for different materials can be satisfied simultaneously.

Evolutionary topology optimization of continuum structures with stress constraints

In this work, we propose to extend the bi-directional evolutionary structural optimization (BESO) method for compliance minimization design subject to both constraints on volume fraction and maximum von Mises stress. To this end, the aggregated p-norm global stress measure is first adopted to approximate the maximum stress. The conventional compliance design objective is augmented with p-norm stress measures by introducing one or multiple Lagrange multipliers. The Lagrange multipliers are employed to yield compromised designs of the compliance and the p-norm stress. An empirical scheme is developed for the determination of the Lagrange multipliers such that the maximum von Mises stress could be effectively constrained through the controlling of the aggregated p-norm stress. To further enforce the satisfaction of stress constraints, the stress norm parameter p is assigned to a higher value after attaining the objective volume. The update of the binary design variables lies in the computationally efficient sensitivity numbers derived using the adjoint method. A series of comparison studies has been conducted to validate the effectiveness of the method on several benchmark design problems.

STRESS-CONSTRAINED TOPOLOGY OPTIMIZATION BASED ON IMPROVED BI-DIRECTIONAL EVOLUTIONARY OPTIMIZATION METHOD

It is necessary to limit maximum nominal stress for engineering structural design generally, so as to avoid that the failure of fracture or fatigue occurs. Topology optimization approach is a feasible strategy. The conventional bi-evolutionary structural optimization (BESO) method cannot effectively address the topology optimization problem with stress constraint. To overcome this limitation, this paper suggests an improved BESO method for stress-constrained topology optimization, in which the minimum compliance design problem with volume and stress constraints is considered. A global stress measure based on the K-S function is introduced to reduce the computational cost associated with the local stress constraint. Meanwhile, the stress constraint function is added to the objective function by using the Lagrange multiplier method. Moreover, the appropriate value of the Lagrangian multiplier is then determined by a bisection method so that the stress constraint is satisfied. The model of BESO method for solving stress-constrained topology optimization and its sensitivity analysis are detailed. Finally, three typical topology optimization examples are performed to demonstrate the validity of the present method, in which the stress constrained designs are compared with the traditional stiffness based designs to illustrate the merit of considering stress constraint. The optimized results indicate that the improved BESO method, as a robust algorithm with stable iterative history, achieves an ambiguous topology with clearly defined boundaries, and realizes a design that effectively reduces stress concentration effect at the critical stress areas.

Stress-based topology optimization using bi-directional evolutionary structural optimization method

This work proposes an evolutionary topology optimization method for stress minimization design using the bi-directional evolutionary structural optimization (BESO) method. The discrete nature of the BESO method avoids naturally the well-known “singularity” problem in density-based methods with degenerated materials. The p-norm stress aggregation scheme is adopted for the measure of global stress level. A computationally efficient sensitivity number formulation is derived from the adjoint sensitivity of the global stress measure. With regard to the highly nonlinear stress behavior, both sensitivity numbers and topology variables are filtered to stabilize the optimization procedure; meanwhile, the filtered sensitivity numbers are further stabilized with their historical information. The method has been shown efficient, practical and easy-to-implement through a series of 2D and 3D benchmark designs.