Stress-Constrained Topology Optimization Using Approximate Reanalysis with on-the-Fly Reduced Order Modeling

Most of the methods used today for handling local stress constraints in topology optimization, fail to directly address the non-self-adjointness of the stress-constrained topology optimization problem. This in turn could drastically raise the computational cost for an already large-scale problem. These problems involve both the equilibrium equations resulting from finite element analysis (FEA) in each iteration, as well as the adjoint equations from the sensitivity analysis of the stress constraints. In this work, we present a paradigm for large-scale stress-constrained topology optimization problems, where we build a multi-grid approach using an on-the-fly Reduced Order Model (ROM) and the p-norm aggregation function, in which the discrete reduced-order basis functions (modes) are adaptively constructed for both the primal and dual problems. In addition to reducing the computational savings due to the ROM, we also address the computational cost of the ROM learning and updating phases. Both reduced-order bases are enriched according to the residual threshold of the corresponding linear systems, and the grid resolution is adaptively selected based on the relative error in approximating the objective function and constraint values during the iteration. The tests on 2D and 3D benchmark problems demonstrate improved performance with acceptable objective and constraint violation errors. Finally, we thoroughly investigate the influence of relevant stress constraint parameters such as the coagulation factor, stress penalty factor, and the allowable stress value.

Economic Stress and Body Weight During the COVID-19 Pandemic

The COVID-19 pandemic has caused income loss for many households, disrupting food consumption patterns and contributing to weight loss for some, and weight gain for others. In this article, I build a dynamic theoretical model that explains those empirical facts. The novelty of this paper is to incorporate stress caused by a lower than ideal income (economic stress) in a model of optimal intertemporal food consumption decisions made by a rational eater. In this framework, economic stress causes disutility and individuals can cope by increasing high-calorie food consumption (stress eating). The limitation to this coping mechanism is that being overweight from excessive calorie intake also decreases utility. Thus, a decrease in income causes updates of the constraints faced by rational consumers of food, which are a budget constraint, a stress constraint and a weight gain constraint. As a consequence, the effect of a decrease in income on body weight reflects a competing income effect as well as two effects specific to economic stress, which are an intertemporal substitution effect and a stress eating effect. Those effects explain opposite weight patterns observed during the pandemic. JEL Classification: D11, D91, I12, I14

Topological Design of Multi-Material Compliant Mechanisms with Global Stress Constraints

This paper presents an approach for the topological design of multi-material compliant mechanisms with global stress constraints. The element stacking method and the separable stress interpolation scheme are applied to calculate the element stiffness and element stress of multi-material structures. The output displacement of multi-material compliant mechanisms is maximized under the constraints of the maximum stress and the structural volume of each material. The modified P-norm method is applied to aggregate the local von Mises stress constraints for all the finite elements to a global stress constraint. The sensitivities are calculated by the adjoint method, and the method of moving asymptotes is utilized to update the optimization problem. Several numerical examples are presented to demonstrate the effectiveness of the proposed method. The appearance of the de facto hinges in the optimal mechanisms can be suppressed effectively by using the topology optimization model with global stress constraints, and the stress constraints for each material can be met.

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

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.

Structurally Constrained Aerodynamic Adjoint Optimisation of Highly Loaded Compressor Blades

Adjoint aerodynamic optimisation has recently gained increased popularity for turbomachinery applications due to the large number of parameters that can be used without incurring additional major computational costs. This work presents an adjoint based aero-structural optimisation method having efficiency as the objective function and maximum von Mises stress set as a constraint. The full optimisation loop was set up with free-form deformation for geometry parametrisation. A response surface was created beforehand for computing the maximum von Mises stress using a meshless method. A discrete adjoint approach was used to obtain the gradients of the objective function with respect to each design parameter, while the constraint gradients were computed using finite differences. A sequential least squares programming algorithm was used as the optimizer. Tests carried out on a highly loaded compressor blade showed that the method successfully increases the efficiency by more than 3% while maintaining the maximum stress under the imposed value. The results also showed that the constrained optimisation loses about 1% in potential efficiency gain compared to the same optimisation process without stress constraint. Overall, the work provides a methodology for conducting structurally constrained adjoint aerodynamic optimisation that can be applied for large number of design parameters while maintaining low computational costs. It also provides reference for constructing and selecting a response surface to be used in the optimisation process.

Analysis of Elasto-plastic Thin-shell Structures using Layered Plastic Modeling and Absolute Nodal Coordinate Formulation

A new elasto-plastic thin shell finite element of the absolute nodal coordinate formulation (ANCF) allowing for large deformation and finite rotation is proposed based on the Kirchhoff-Love theory and layered plastic model. The von Mises yield criterion of plane-stress with linear isotropic hardening is adopted in constitutive description of elasto-plastic material. Owing to the plane-stress constraint, special treatment should be given to the stress update algorithm for plasticity. To accommodate the plasticity formulation, the Gauss-point layered integration is inserted into the thickness of the element to produce the internal force. Then, the Jacobian of internal forces is deduced by deriving the consistent elasto-plastic tangent moduli. To accurately track the load-displacement equilibrium path in the buckling analysis of elasto-plastic thin shells, the arc-length method is used. The dynamics of the thin shells is also studied by using the generalized-alpha algorithm. Finally, several static and dynamic examples are presented to verify the accuracy of the proposed formulation.

A new Hybrid Taguchi-salp swarm optimization algorithm for the robust design of real-world engineering problems

In this paper, a new hybrid Taguchi salp swarm algorithm (HTSSA) has been developed to speed up the optimization processes of structural design problems in industry and to approach a global optimum solution. The design problem is posed for the shape optimization of a seat bracket with a mass objective function and a stress constraint. Objective function evaluations are based on finite element analysis, while the response surface method is used to obtain the equations necessary for objective and constraint functions. Recent optimization techniques such as the salp swarm algorithm, grasshopper optimization algorithm and, Harris hawks optimization algorithm are used to compare the performance of the HTSSA in solving the structural design problem. The results show the hybrid Taguchi salp swarm algorithm’s ability and the superiority of the method developed for optimum product design processes.

Recent Advances of Genetic Resources, Genes and Genetic Approaches for Flooding Tolerance in Rice.

: Flooding is one of the most hazardous natural disasters and a major stress constraint to rice production throughout the world, which results in huge economic losses. The frequency and duration of flooding is predicted to increase in near future as a result of global climate change. Breeding of flooding tolerance in rice is a challenging task because of the complexity of the component traits, screening technique, environmental factors and genetic interactions. A great progress has been made during last two decade to find out the flooding tolerance mechanism in rice. An important breakthrough in submergence research was achieved by identification of major quantitative trait locus (QTL) SUB1 in rice chromosomes that acts as the primary contributor for tolerance. This enabled the use of marker-assisted backcrossing (MABC) to transfer SUB1 QTL into popular varieties which showed yield advantages in flood prone area. However, SUB1 varieties are not always tolerant to stagnant flooding and flooding during germination stage. So, gene pyramiding approach can be used by combining several important traits to develop new breeding rice lines that confer tolerances to different types of flooding. This review highlights the important germplasm/genetic resources of rice to different types of flooding stress. A brief discussion on the genes and genetic mechanism in rice exhibited to different types of flooding tolerance was discussed for development of flood tolerant rice variety. Further research on developing multiple stresses tolerant rice can be achieved by combining SUB1 with other tolerance traits/genes for wider adaptation in the rain-fed rice ecosystems.