Strength Constraints Research Articles

Instability-driven family optimization of cold-formed steel lipped-channel cross-sections with strength and stiffness constraints

The objective of this study is to advance a solution scheme that can produce a family of optimized thin-walled cold-formed steel lipped-channel sections under combined compressive and flexural loading subjected to both strength and stiffness constraints. In this new study, the solution scheme is extended from previous work considering strength constraints only to include stiffness constraints to address the serviceability requirement as well for a more practical reflection of behavior whereby stiffness is reduced due to member instabilities. The stiffness constraint is driven by a novel method for estimating effective moment of inertia due to cross-section instabilities such as local and distortional buckling modes. A two-level optimization framework is utilized to produce a family of optimized sections. The first level focuses on individual member optimization of the P−M demand space as derived from current commercially available lipped-channel sections in the United States; the second level focuses on a new family of optimized sections capable of covering the same design space at a minimal family size. The results of the study show that a family of only 8 unique optimized sections can replace 186 commercially available sections and still achieve the same or improved performance in terms of both strength and stiffness compared to strength constraints only. The developed family of sections demonstrates that optimization techniques, employing complicated design constraints, have a great potential for improving cold-formed steel production on currently widely-used cross-section shapes such as lipped channels.

The effect of mechanical inhomogeneity in microzones of welded joints on CTOD fracture toughness of nuclear thick-walled steel

This study employs the microshear test method to examine the local mechanical properties of narrow-gap welded joints, revealing the mechanical inhomogeneity by evaluating the microshear strength, stress‒strain curves, and failure strain. On this basis, the influence of weld joints micromechanical inhomogeneity on the crack tip opening displacement (CTOD) fracture toughness is investigated. From the root weld layer to the cover weld layer, the fracture toughness at the center of the weld seam demonstrates an increasing trend, with the experimental and calculated CTOD values showing a good correspondence. The microproperties of the welded joints significantly impact the load-bearing capacity and fracture toughness. During the deformation process of the “low-matching” microregions, the plastic zone expansion is hindered by the surrounding microregion strength constraints, thus reducing the fracture toughness. In contrast, during the deformation of the “high-matching” microregions, the surrounding microregions absorb some of the loading energy, partially releasing the concentrated stress at the crack tip, which in turn increases the fracture toughness.

New energy vehicle online selection method considering attribute compensation relationship and aspiration strength

With the development of information technology, online trading platforms for new energy vehicles, represented by Autohome.com, provide individualized decision-making support services for consumers. Considering that consumers often have different attribute requirements when deciding to buy a new energy vehicle. From the requirement information, we can derive the consumers' individual preferences for attribute compensation relationships. This relationship may also indicate, to some extent, that consumers have different strength constraints on different attribute requirements, i.e. aspiration strength. Therefore, to adjust consumers' attribute aspirations and select more products that satisfy consumers’ requirements, this paper investigates how to derive aspiration strength based on the attribute compensation relationship provided by consumers. Specifically, we first define a functional mapping relationship between the attribute compensation relationship and the aspiration strength. According to the mapping relationship, we obtain the aspiration strength. We can change the attribute aspirations based on aspiration strength. Furthermore, attribute compensation relationships are considered to compensate for the product attribute performance. Based on this, we design a new online selection method for new energy vehicles. Finally, a case study of Autohome.com is proposed to verify the effectiveness of the method. We use comparative analysis and random number experiments to demonstrate its robustness and necessity.

Non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the strength constraint parameterized level set method and interval mathematics

In this paper, a study on non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the parameterized level set method (PLSM) is conducted. The P-norm is used to replace the local stress constraint with a single comprehensive stress constraint that approximates the maximum stress to optimize the structure model with minimum volume. In the interval-set model, the stress constraint is transformed into the non-probabilistic reliability-based scheme and the reliability is evaluated by the optimization feature distance (OFD). In the NRBTO scheme, the unknown-but-bounded (UBB) uncertainties of the material and external load of the optimized structure are considered. By interpolating the level set function (LSF) with the multiquadric (MQ) splines, the partial differential equation (PDE) is transformed into an ordinary differential equation (ODE). In addition, the interval parameter vertex method is employed to obtain the stress constraint interval, and the shape derivative and adjoint vector methods are used to obtain the evolution velocity field of LSF. The optimality criterion (OC) method is used to solve the optimization problem. Finally, three examples are given, and the optimization model of stiffness constraint is introduced, which not only verifies the applicability of the topology optimization scheme based on non-probabilistic reliability but also compares the difference between the topology optimization with strength constraint and the topology optimization with stiffness constraint.

Optimized Lightweight Frame for Intelligent New-energy Vehicles

In this paper, a joint optimization method based on multi-objective response surface approximation model and finite element simulation program is proposed to realize the lightweight optimization of new-energy vehicle frames. Under the premise of satisfying the constraints of strength, frequency and vibration, the thickness of different important parts is optimized to achieve the goal of minimizing the quality of intelligent vehicles. In order to obtain the stress distribution of each part and the vibration frequency of the frame, various finite element analyses of the intelligent vehicle frame are analyzed. In order to achieve optimization, this paper adopts the response surface method for multi-objective optimization. Sample data was generated by the central composite design, and the response surface optimization method was used to filter out 5 design variables that had a large impact on the frame. As a result, the weight of the frame was reduced from 25.05 kg to 19.86 kg, a weight reduction of 20.7%, achieving a significant weight reduction effect. This method provides important reference value and guiding significance for the optimization of frame and its lightweight. In this way, the design of the frame can be better optimized to make it lighter, thereby improving the performance of the smart car. At the same time, this method can also be applied to optimization problems in other fields to achieve more efficient and accurate optimization goals.

Investigation on nonlinear buckling performance of the optimized wing structure under the realistic flight cases

The nonlinear finite element simulation is a standard technique for structural stability analysis, whereas it still has disadvantages of highly computational cost and poor convergence, especially for the large and complex wing structure. In this paper, nonlinear buckling analysis of a wing structure is performed and focused on the local region that is prone to instability, the boundary conditions of which are determined using the sub-modeling technique and realistic flight conditions of an aircraft. Firstly, the flight envelope is calculated based on the preliminary parameters of a large aircraft. Three typically flight cases of the aircraft are selected and the corresponding aerodynamic loads are achieved. Then, an optimization problem with strength and deformation constraints is defined to minimize the weight of the wing structure under the design limit load. A significant reduction in structural weight is achieved by considering three typically flight cases in the optimization process. Next, linear structural analyses come to a conclusion that the upper skin of the wing butt box located between the inner and outer wings is easy to lose stability. The sub-modeling technique is used to extract the local model of the wing butt box from the global model of the wing structure. A nonlinear buckling analysis is performed on the local model by applying the realistic boundary conditions solved from the global model. The skin depressions produced by buckling are carefully studied. Finally, the wing upper skin is reinforced by assigning the stringers to increase the buckling resistance of the structure. The appearance of the skin depressions is significantly postponed, meanwhile the depth is largely reduced.

Application research in multi-objective constrained optimization of composite wing structure

In order to explore the optimization of composite wing structure, this paper reviews the past research works of optimization of composite wing structures worldwide and in China. It concludes that most optimization methods and calculations are useful but only applied with specified theoretic model. Then relevant composite optimization theories and strength constraints with composite lamination failure criteria, stability, aeroelasticity are sorts out. Optimizing algorithm and applied solution rounding strategy are also listed. Concentrating on weight-reduction analysis on the thickness, sequence, and angle of the composite stacking under multiple constraints, a practical model of a composite wing structure example with a large aspect ratio is completed, and the calculation is based on the finite element analysis tool Nastran and the genetic algorithm Matlab program. Two optimal solutions are given with detailed differences and the comparison of the composite structure parameters before and after calculation is also recorded. The application example indicates the feasibility of the optimization method and quadratic rounding process, the detail structure performance improvements with skin lamination change under the calculation are illustrated at the same time.

In search of the quasi-isotropic laminate with optimal delamination resistance under off-axis loads

Delamination is one of the most feared failure modes in laminated composites and yet there is a lack of well established procedures to find the ply configuration with the highest delamination resistance for a given geometry of the component and a set of elastic and strength constraints. This paper presents a methodology for determining the quasi-isotropic ply sequence more resistant to delamination under off-axis uniaxial tension. Delamination is considered to be triggered by interlaminar stresses at free-edges or by matrix cracks. Two different ply thicknesses (standard and thin) and two sets of ply orientations (multiples of π/4 or π/8) are considered. The results show that the use of thin plies enlarges the design domain by up to 70% and generates a practically isotropic safe space. The methodology presented is also suitable for optimizing the delamination resistance of other load cases with stress singularities.

On Design Challenges of Portable Nuclear Magnetic Resonance System

This article studies the optimal design approach for a portable nuclear magnetic resonance (NMR) system for use in non-destructive flow measurement applications. The mechanical and electromagnetic design procedures were carried out using the Ansys Maxwell finite-element analysis (FEA) software tool. The proposed procedure considered homogeneity and strength constraints while ensuring the desired functionality of the intended device for a given application. A modified particle swarm optimization (MPSO) algorithm was proposed as a reference design framework for optimization stages. The optimally designed NMR tool was prototyped, and its functionality was validated via several case studies. To assess the functionality of the prototyped device, Larmor frequency for hydrogen atom was captured and compared with theoretical results. Furthermore, the functionality and accuracy of the prototyped NMR tool is compared to the off-the-shelf NMR tool. Results demonstrated the feasibility and accuracy of the prototyped NMR tool constrained by factors, such as being lightweight and compact.

Automated minimum-weight sizing design framework for tall self-standing modular buildings subjected to multiple performance constraints under static and dynamic wind loads

In recent decades, the shortage of affordable housing has become an endemic issue in many cities worldwide due to the ongoing urban population growth. Against this backdrop, volumetric steel modular building systems (MBSs) are becoming an increasingly compelling solution to the above challenge owing to their rapid construction speed and reduced upfront costs. Notwithstanding their success in low- to mid-rise projects, these assembled structures generally rely on a separate lateral load-resisting system (LLRS) for lateral stiffness and resistance to increased wind loads as the building altitude increases. However, additional LLRSs require on-site construction, thereby compromising the productivity boost offered by the MBSs. To this end, this paper proposes a novel optimisation-driven sizing design framework for tall self-standing modular buildings subjected to concurrent drift, floor acceleration, and member strength constraints under static and dynamic wind loads. A computationally efficient solution strategy is devised to facilitate a meaningful sizing solution by decomposing the constrained discrete sizing problem into a convex serviceability limit stage (SLS) and a non-convex ultimate limit stage (ULS), which can be then solved using preferred local and global optimisation methods, separately. The framework is implemented by integrating SAP2000 (for structural analysis) and MATLAB (for optimisation) through SAP2000′s open Application Programming Interface (API), and demonstrated using a 15-storey self-standing steel modular building exposed to three different levels of wind intensity. A comprehensive performance assessment is conducted on the optimally designed case-study building to investigate its elastic instability behaviour, geometric nonlinear effects on wind-induced response, and impacts of global sway imperfections on member utilisation ratios under wind effects. It is concluded that tall self-standing modular buildings can be achieved economically using ordinary corner-supported modules without ad hoc structural provisions, while consuming steel at similar rates to conventional building structural systems. Furthermore, the proposed sizing framework and solution strategy have proven to be useful design tools for reconciling the structural resilience and material efficiency in wind-sensitive self-standing modular buildings.

Shear transfer strength of alkali-activated slag-based concrete

As a part of ongoing research to apply alkali-activated slag-based concrete in building structures, the shear transfer behavior of alkali-activated slag-based concrete was experimentally examined through the push-off tests of 32 initially uncracked reinforced planes. The test parameters were concrete type, concrete strength, shear reinforcement ratio, and shear plane size. The test results and comparative analysis showed that the shear strength of reinforced alkali-activated slag-based concrete (AAC) was comparable to Portland cement concrete (PCC) counterparts. However, AAC planes cracked earlier and displayed larger crack separation at the peak load, which is attributed to higher cracking prevalence and brittleness of AAC. Both the increase of concrete strength and lateral constraint stress promotes the development of shear strength in reinforced planes, and their effect is interactional. The shear strength decreased as the shear plane width and depth increased. The existing strength models from design codes and literatures for the shear transfer strength of PCC are still applicable to reinforced AAC planes. Among them, AASHTO LRFD Bridge Design Specifications and the nonlinear model proposed by Mau and Hsu gave better predictions of the measured shear strengths of AAC.

An efficient differential evolution-based method for optimization of steel frame structures using direct analysis

Sizing optimization of steel frames using direct analysis is a highly complex optimization problem with discrete design variables and highly nonlinear constraints of structural safety and serviceability conditions. To tackle this problem, this study develops an improved differential evolution (DE), namely 2EpDE, with a new mutation technique using two p-best individuals. The results of twenty benchmark functions and four real-world constrained optimization problems prove that 2EpDE effectively saves computational efforts and searches for better global optimal solutions. A framework for the optimization of steel frames is then proposed using a combination of 2EpDE, Multi-Comparison Technique (MCT), and Promising Individual Method (PIM). The strength and serviceability constraints of the optimization are evaluated by direct analysis that can accurately perform the nonlinear inelastic behaviors of the structure. Two examples including two-story and six-story space frames are optimized to evaluate the efficiency of the proposed method. Compared to Jaya and Particle Swarm Optimization (PSO), the proposed method can save more than 35% of computational efforts and yields better optimum results.

Prestress and size optimization of double-curvature cable domes using an incremental-prestressing iterative technique

A major challenge in designing new forms of cable domes is to keep balance between structural weight and stiffness. Increasing prestress level should decrease the maximum displacement and this, in turn, may lead to heavier structures and higher costs. Accordingly, the required cross sections and prestress level that achieve stability and strength constraints vary whenever this weight-stiffness balance changes, typically as moving along a Pareto front that represents the solution of a two-objective optimization of weight and displacement. Apart from complicated derivation of the gradient of optimization function or using time-consuming gradient-free optimization algorithms, this study proposes a time-efficient iterative technique aims at developing a trade-off curve between the optimized weight and corresponding displacement of cable domes that simulates the Pareto front solution of two-objective optimization. This curve provides insights into the extent to which the optimized weight would increase when decreasing the maximum displacement, giving the designer a decision support tool to select the most preferred solution. The proposed technique is based on prestressing the dome with an appropriate initial level of prestress, then increasing the level of prestress incrementally until reaching the target stiffness. By each increment of prestress level, the dome is designed to the minimum weight that achieves the stability and strength constraints through sub-iterations. The variables of this incremental-prestressing (IP) iterative technique are prestress level and size of elements with constraints on stability of struts and strength of cables. The resulting pairs of optimized weight and corresponding displacement at all increments of prestress level are, then, fitted to a power function formulating the trade-off curve. The proposed IP technique is used to design a simple illustrative example as well as a realistic double-curvature cable dome. The efficiency of the proposed technique is verified by comparing the resulting trade-off curve of cable dome example to the Pareto optimal solutions obtained by a two-objective optimization of weight and displacement using NSGA-II algorithm. Different geometrical parameters are considered to highlight the time-efficiency of the IP technique for further usage as a robust tool in large parametric studies in which surrogate functions are developed to predict the optimized weight and prestress level of cable domes at specific target stiffness.

Topology optimization for additive manufacturing with strength constraints considering anisotropy

Abstract Combining topology optimization and additive manufacturing (AM) is a promising approach to breaking through the limitations of conventional design and developing innovative structures with high performance. However, the unique manufacturing constraints in AM should be considered when developing the topology optimization algorithms for AM. Material anisotropy is one of the common characteristics of AM materials due to the layer-by-layer manufacturing techniques. This work proposes a topology optimization approach for AM with strength constraints considering anisotropy. The Hoffman failure criterion is adopted to represent the anisotropic strength behaviors of AM materials. Based on the Hoffman failure criteria and the p-norm measure aggregation function, a global strength constraint formulation is established. Under the framework of solid isotropic material with penalization, we develop a topology optimization methodology to minimize the structural weight or volume fraction subject to structural stiffness and strength constraints. Several two-dimensional (2D) or 3D numerical test cases are performed to validate the effectiveness and performance of the developed method. The results indicated that the proposed method could make full use of material properties by considering anisotropic strength. Besides, the topological optimization considering strength anisotropy could be combined with build direction optimization to further reduce the structural weight.

Optimization of composite plates with viscoelastic damping layer for high sound transmission loss under stiffness and strength constraints

Optimization of composite plates with viscoelastic damping layer for high sound transmission loss under stiffness and strength constraints

3D printing of polylactic acid: recent advances and opportunities.

Bio-based polymers are a class of polymers made by living organisms, a few of them known and commercialized yet. Due to poor mechanical strength and economic constraints, they have not yet seen the extensive application. Instead, they have been an appropriate candidate for biological applications. Growing consumer knowledge of the environmental effect of polymers generated from petrochemical sources and a worldwide transition away from plastics with a lifespan of hundreds of years has resulted in greater interest in such hitherto unattainable sectors. Bio-based polymers come in various forms, including direct or "drop-in" replacements for their petrochemical counterparts with nearly identical properties or completely novel polymers that were previously unavailable, such as polylactide. Few of these bio-based polymers offer significantly improved technical specifications than their alternatives. Polylactic acid (PLA) has been well known in the last decade as a biodegradable thermoplastic source for use in 3DP by the "fused deposition modeling" method. The PLA market is anticipated to accomplish 5.2 billion US dollars in 2020 for its industrial usage. Conversely, 3DP is one of the emerging technologies with immense economic potential in numerous sectors where PLA is one of the critical options as the polymer source due to its environmentally friendly nature, glossiness, multicolor appearance, and ease of printing. The chemical structure, manufacturing techniques, standard features, and current market situation of PLA were examined in this study. This review looks at the process of 3DP that uses PLA filaments in extrusion-based 3DP technologies in particular. Several recent articles describing 3D-printed PLA items have been highlighted.

Composite Lamina Model Design with the Use of Heuristic Optimization.

In engineering practice, a problem is quite often faced in which the number of unknown parameters exceeds the number of conditions or requirements or, otherwise, there are too many requirements for too few parameters to design. Such under- or over-defined tasks are sometimes not possible to solve using a direct approach. The number of solutions to such problems is multiple, and it is most rational to search for the optimal one by numerical methods since the more unknown design parameters there are to be designed, the more potential solutions there are. This article discusses a way to find an optimal solution to such an underdetermined problem by heuristic optimization methods on the basis of the example of designing a composite wing skin of an aircraft. Several heuristic approaches, specifically gradient descent and Tabu search, are studied to solve the design problem and to locate an optimal solution. They are also compared to a conventional direct approach. The examined composite lamina is optimized by the target function of minimum weight with the constraints of strength and buckling failure criteria. In most of the observed cases, the heuristic method designed structures which were considerably better than the structures that were obtained by conventional direct approaches in terms of the weight to load ratio.

Research on tracking and decomposing method of aerobics movement based on machine learning

In order to overcome the low success rate of tracking and decomposing traditional aerobics movement tracking and decomposition method, this paper proposes a method of aerobics action tracking and decomposition based on machine learning. In this method, a multi-layer pyramid structure is built to segment the aerobics video image, and the key frame and the frame with the highest energy value are detected to obtain the binary image. This paper constructs a standardised tracking target model, uses convolution filter to detect multi-objective feature vectors in the image, uses binary classifier to build machine learning framework, and realises aerobics action tracking decomposition under the vector constraints of impact strength, spatial and frequency domain vectors. The experimental results show that this method can effectively deal with the interference from the external environment in partial sequence tracking, and compared with the traditional method, this method has higher success rate of tracking and decomposition and has reliability.

Custom software development of structural dimension optimization software for the buckling of stiffened plates

<abstract> <p>Existing structural optimization software tools only integrate the Euler buckling function of rods and plates and do not consider the buckling strength constraint of stiffened plates, thus failing to meet the optimization design requirements of thin-walled structures such as ship hulls. In this study, according to the buckling strength specifications for stiffened plates of ships, the custom software development of a structural optimization program with "buckling constraints of stiffened plates" was performed using the HyperMesh optimization design software. The finite-element grid of the stiffened plate was divided; the average stress, stress gradient and other parameters associated with the buckling of stiffened plates were determined; the DRESP3 card was set; the external OML function file was linked and the buckling strength of the stiffened plates was introduced into the dimensional optimization design model as a constraint. The proposed method was used to optimize the structure scantlings of a platform, achieving a reduction of 8.96% compared with the original scheme, while also meeting the requirements of structural strength, deformation and buckling strength. The results demonstrated that the dimensional optimization software with buckling constraints is operable and can aid in the rapid structural optimization design of stiffened plates.</p> </abstract>

An intelligent decision support system for solving optimized geometric design problems

An integrated intelligent approach for solving geometric design problems is studied. A general optimization placement problem of arbitrary shaped objects in a bounded container is formulated as a mathematical programming problem in terms of the phi-function technique. Various technological requirements (geometric and mechanical) are considered, including continuous translations and rotations of the objects, allowable distances between objects, prohibited zones in the container, balancing conditions, mechanical strength constraints. Solution strategies, methods, and algorithms to solve different variants of the model are discussed and illustrated with examples.