Displacement Constraints Research Articles

A programmable modular lattice metamaterial with multiple deformations

This paper describes a class of lattice metamaterials with tunable mechanical properties controlled by the material modulus and structural parameters of the cellular units. The deformation shapes can also be changed by external control. We have developed 3D printed quadrilateral cellular TPU units with specially shaped edge walls. A simplified mechanical model of the different cell deformation processes is established and verified by numerical simulations and experiments. On this basis, by tessellating and matching these transformations together, we create assembly grids with adjustable stiffness and deformation shapes controlled by thermal and displacement constraints.

Thermal Stress Compensation for an Aircraft Engine Duct System Based on a Structural Redesign of Tie Rods

The reliability of the aircraft engine duct system is of paramount importance as it directly affects the safety of the aircraft, particularly under high-temperature and high-pressure cycles. In this study, ANSYS Workbench was used for finite element analysis, and a sleeve-type tie rod structure was proposed to address the critical problem of tie rod tearing during the operation of the duct system, thereby optimizing thermal stress compensation for the duct system. The research results show the following: (1) The anchor of the traditional tie rod imposes displacement constraints on the thermal deformation of the duct system, leading to stress concentration and even structural failure in the connection area between a duct and a tie rod. (2) The improved sleeve-type tie rod provides greater axial displacement freedom for the duct, effectively mitigating stress concentration phenomena. (3) Taking a worst-case scenario of 537.78 °C and 2 MPa as an example, the sleeve-type tie rod proposed in this paper can reduce the stress at the tie rod connection from 757.61 MPa to less than 25 MPa, a reduction of more than 96%. The original tie rod tearing problem is solved, and the maximum stress of the whole duct system is reduced to 459.25 MPa, which is below the yield strength.

Event-based singularity-free fixed-time fuzzy control for active suspension systems with displacement constraint

Event-based singularity-free fixed-time fuzzy control for active suspension systems with displacement constraint

A comparison performance analysis of eight meta-heuristic algorithms for optimal design of truss structures with static constraints

Metaheuristics have been successfully used for solving complex structural optimization problems. Many algorithms are proposed for truss structure size and shape optimization under some constraints. This study considers eight population-based meta-heuristic methods: African Vultures Optimization Algorithm (AVOA), Flow Direction Algorithm (FDA), Arithmetic Optimization Algorithm (AOA), Generalized Normal Distribution Optimization (GNDO), Stochastic Paint Optimizer (SPO), Chaos Game Optimizer (CGO), Crystal Structure Algorithm (CRY) and Material Generation Algorithm (MGO). These meta-heuristics methods are used to optimize the size of three aluminum truss structures. Optimization aims to reduce the weight of the truss members while meeting a set of displacement and stress constraints. The performance of these methods is assessed by solving and optimizing three well-known truss structure benchmarks under some constraints. The results show that the Stochastic Paint Optimizer (SPO) outperforms the other algorithms in terms of accuracy and convergence rate.

Unified buckling computational framework of hydro-statically-loaded stiffened composite cylindrical shells

In this research, a unified computational framework was developed to analyze the complex multiple buckling modes of stiffened cylindrical shells under hydrostatic pressure, and avoid the complex process of calculating multiple buckling modes separately by traditional methods. The stiffener-shell displacement constraints were analyzed through introducing stress distribution to the shell. The minimum potential energy principle was adopted for the buckling load solution. The framework can predict the overall buckling, tripping, and coupled shell-stiffener buckling simultaneously, and reveal the relationship between buckling modes and structural dimensions. The unified framework is more convenient and saves computational resources compared with the finite element method. Based on this new method, the buckling mode transition characteristics under simply- and fixed-supported boundary conditions were discussed. An energy-based criterion was proposed to evaluate the occurrence condition of each buckling mode. The research provides a reference for the design of submerged composite stiffened cylindrical shells.

Manufacturing-Cost-Driven Topology Optimization of Welded Frame Structures

Abstract This work presents a method for the topology optimization of welded frame structures to minimize the manufacturing cost. The structures considered here consist of assemblies of geometric primitives such as bars and plates that are common in welded frame construction. A geometry projection technique is used to map the primitives onto a continuous density field that is subsequently used to interpolate material properties. As in density-based topology optimization techniques, the ensuing ersatz material is used to perform the structural analysis on a fixed mesh, thereby circumventing the need for re-meshing upon design changes. The distinct advantage of the representation by geometric primitives is the ease of computation of the manufacturing cost in terms of the design parameters, while the geometry projection facilitates the analysis within a continuous design region. The proposed method is demonstrated via the manufacturing-cost-minimization subject to a displacement constraint of 2D bar, 3D bar, and plate structures.

Static and dynamic analysis of the postbuckling of axially moving spin beams

This paper aims to investigate the static and dynamic behaviors of the postbuckling of axially moving spin beams (bi-gyro system). The Hamilton’s principle is used to derive the nonlinear governing equations of bi-gyro systems, which are based on the Euler-Bernoulli beam model and account for von Karman geometric nonlinearity. After neglecting the time-dependent terms, the static equations are discretized using the differential quadrature method and then solved as a nonlinear algebraic system via the Newton-Raphson iteration method. Subsequently, the linear vibration problem is accurately solved for axially moving spinning beams in their first buckled configuration. Finally, numerical calculations are conducted to investigate the impact of axial and spinning velocities on the steady-state dynamic responses of bi-gyro systems. The findings are as follows: (a) the critical axial velocity where trivial equilibrium is unstable remains unaffected by the presence of spinning velocity; (b) the bifurcation point of the axial velocity corresponding to amplitude is reduced by spinning velocity, resulting from centrifugal force; (c) the vibration amplitude of the bi-gyro system will diverge under a weaker displacement constraint spring; and (d) stable buckled and straight configurations can coexist under certain axial and spinning velocities.

Swarm intelligence hybridized with genetic search in multi-objective design optimization under constrained-Pareto dominance

The inclusion of uncertainty in structural design optimization led to more complex design optimization formulations, where uncertainty quantification has significant influence on solution methods and computing times. Designs maintaining steady levels of performance, under uncertainty, are called robust and the combination of both robustness and performance optimality leads to a methodology called Robust Design Optimization (RDO). In this work a new approach to the RDO of angle-ply composite laminate structures is proposed. The key concept of this methodology is the hybridization between the principles of Particle Swarm Optimization and Genetic Algorithms, through the evolution of multiple populations based on local and global constrain-dominance. The RDO problem is here defined as the bi-objective minimization of the structural weight (optimality) and the determinant of the variance–covariance matrix (robustness) of the system’s response functionals, subject to stress and displacement constraints. A numerical structural design problem, representing a composite laminate engine hood shell, shows the capabilities of the proposed approach. Results display the good convergence properties of the proposed hybridizations both in the search and objective spaces.

Optimization of framed structures subjected to blast loading using equivalent static loads method

In this study, the optimum design of a three-dimensional framed steel structure subjected to blast loading is considered. The main idea of this research is to develop a practical formulation for the design optimization problem and to study the effect of including blast loads in the design process. The optimization problem is formulated to minimize the total weight of the structure subjected to American Institution of Steel Construction (AISC) strength requirements and blast design displacement constraints. The design variables for beams and columns are the discrete values of the W-shapes selected from the AISC tables. A car carrying 250 lbs of trinitrotoluene with a 50 ft standoff distance from the front face is modeled as the source of the blast loading. Pressure–time histories are calculated on the front, sides, roof, and rear faces of the structure. Since the problem functions are not differentiable with respect to the design variables, the gradient-based optimization algorithms cannot be used to solve the problem. Therefore, metaheuristic algorithms are used to solve the optimization problem. Linear and nonlinear dynamic analyses are carried out in the optimization process. The problems are solved using metaheuristic optimization with the equivalent static loads method (MOESL). In MOESL, the dynamic load is transformed into equivalent static loads (ESLs) then the linear static analysis is carried out in the optimization process. The problems are 4-bay × 4-bay × 3-story frames under serviceability and blast loading. It is shown that a penalty on the optimum structural weight is substantial for designing structures to withstand blast loads.

Enhancing heat dissipation and mass transfer of oxygen gas flow channel in a proton exchange membrane fuel cell using multiobjective topology optimization

To enhance the heat dissipation and mass transfer from a proton exchange membrane fuel cell (PEMFC) stack, a multi-objective topology optimization model considering structural deformation, heat transfer, mass diffusion, and gas flow process is proposed herein. The average molar concentration of oxygen and average temperature in the cathode catalyst layer (CL) are considered as the optimization objectives, and the mechanical, mass transfer, and gas flow properties are treated as constraints. The results reveal that compared with a straight gas channel, the topology-optimized configuration leads to an improvement in oxygen molar concentration by 10.36% and reduction in average temperature by 2.26 K. A higher power-dissipation constraint leads to a more complex three-dimensional channel structure with more branches. A larger structural displacement constraint results in a wider and flatter flow channel topology. The average oxygen molar concentration of topologically optimized configurations increases ranging from 5.18 to 14.96%, and the average temperature in the CL decreases about 2.2 K, compared with that of straight gas channel configurations, when the velocity at inlet varies from 0.05 to 0.3 m/s. These findings can aid in the design of PEMFCs.

Optimal Design of Planar Steel Frames Using the Hybrid Teaching–Learning and Charged System Search Algorithm

In this study, a novel effective algorithm called HTC which results from a hybridization process between the teaching–learning-based optimization (TLBO) and charged system search (CSS) algorithms is proposed and utilized to optimize planar steel frames. Among the features of the proposed algorithm, simplicity and low number of setting parameters can be mentioned. The main goals of this hybridization process are to establish a balance between exploration and exploitation, increase the rate of convergence, and avoid getting trapped in the local optimal point. Moreover, the purpose of optimizing steel frames is to calculate their minimum weight by choosing suitable sections as well as considering the stress and displacement constraints in accordance with the requirements of the AISC design regulations using the load and resistance factor design (LRFD) method. To evaluate the performance of the HTC algorithm, standard benchmark steel frames are examined, and the results of the proposed algorithm are compared with other metaheuristic optimization methods. According to the outcomes of the comparison, the proposed algorithm has better performance than the other methods.

A hybrid direct FE2 method for modeling of multiscale materials and structures with strain localization

Strain localization is a common phenomenon existing in various multiscale materials or structures, e.g., the bulking bands of thin-walled structures, the local collapse of porous materials, and the crack in solid materials, etc. However, this phenomenon cannot be captured by the conventional homogenization methods, such as mean-field homogenization (e.g., Mori–Tanaka method), first-order or high-order computational homogenization (e.g., the Finite Element Square method), etc., due to the high strain gradient associated with strain localization. Aiming at this, a hybrid Direct FE2 method is proposed by combining the D-FE2 (Direct FE2) and the traditional FE methods, while the multiscale structure is modeled using the D-FE2 method in the region exhibiting low deformation gradient, and the other region displaying high deformation gradient is modeled using the traditional FE method. Moreover, a node displacement constraint and an overall node displacement constraint derived from the multilevel equilibrium equations using the Gauss–Ostrogradsky theorem are respectively prescribed to the interface between the D-FE2 model and the FE model of the multiscale structure, to enforce the energy equilibrium and deformation continuity. The proposed hybrid D-FE2 method is then applied to predict the strain localization behavior of multiscale materials or structures, including local bulking of honeycomb structures, in-situ crack propagation, and localized plastic deformation in fiber reinforced composites, etc. Comparison of the simulation results obtained from the hybrid D-FE2 method and the traditional FE method validates the accuracy, efficiency and ease of numerical implementation of the proposed hybrid D-FE2 method.

Τopology Optimization under a Single Displacement Constraint Using a Strain Energy Criterion

Based on a previous concept that has been successfully applied to the sizing optimization of truss and frame structures, this work extends and improves the strain energy criterion in the topology optimization of 2D continuum structures under a single displacement constraint. To make the proposed methodology transparent to other researchers and at the same time meaningful, the numerical value of the displacement constraint was taken to be equal to that obtained through the well-known Solid Isotropic Material with Penalization (SIMP) method under the same boundary conditions and the same external forces. The proposed method is more efficient than the SIMP method while leading to topologies very close to those obtained by the latter.

Observer Based Adaptive Neural Networks Fault-Tolerant Control for Pneumatic Active Suspension With Vertical Constraint and Sensor Fault

This paper treats the problem of a pneumatic active suspension considering uncertain parameters and displacement constraints under the presence of sensor failure and unmeasured states. A quarter car model is established using an air spring to provide flexible stiffness and an active force to suppress the chassis vibrations. To approximate unknown nonlinear functions of pneumatic actuator dynamic, neural networks are employed as a function approximator. The sensor fault is investigated while all system states of the controlled suspension are assumed to be unmeasurable. Then, a neural state observer is constructed to estimate unmeasured states and compensate for the partial loss of effectiveness of sensor failure simultaneously. An adaptive fault tolerant control is proposed via the command filter backstepping technique to alleviate the effects of sensor failure and solve the explosion of complexity problem. In addition, to improve the tracking accuracy and get the ride comfort, this study is concerned with a prescribed performance function so that the vertical displacement of sprung mass does not violate the predefined boundary. The Lyapunov theorem is then applied to demonstrate that all system signals are semi-globally uniformly ultimately bounded while error variables can converge to the small neighborhood of zero. Finally, comparative simulation examples are analyzed to verify the effectiveness of the designed control with sensor noise and unmeasurable variables.

Development of model-based and model-free reactive control scheme: considering copper loss and movable-floater-displacement constraint for a wave energy converter

The utilization of wave energy is expected since ocean wave energy has a high potential. The improvement of the feasibility of wave energy converters requires control that maximizes the electric output energy, including the copper loss under a displacement constraint. Several model-based and model-free reactive controls have been developed. Although model-based reactive control attains high performance, it struggles to deal with modeling errors and forecasting wave excitation forces. On the other hand, the model-free reactive control can adapt to dynamic modeling, including modeling errors; however, it requires a vast amount of learning data and considerable time and effort to consider the displacement constraint. Model-based and model-free reactive controls each have advantages and disadvantages. Combined model-based and model-free reactive controls are desirable to freely switch between the model-based and model-free reactive controls based on various ocean situations. In this study, two equivalent model-based and model-free reactive controls that can consider the copper loss and displacement constraints without forecasting the wave excitation forces were proposed. The model-free reactive control was compared with the model-based reactive control and a conventional control using numerical simulations in irregular waves. The results of the simulation show that the proposed model-based reactive control achieves superior performance compared to that of the conventional control. The proposed model-free reactive control achieved comparable performance to that of the proposed model-based reactive control under various wave conditions. Moreover, the proposed model-free reactive control decreased the required training trials. The development of the two equivalent control schemes will lead to the proposal of combined model-based and model-free reactive controls in the future.

Teaching-learning-based optimization of unbraced steel frames with semi-rigid connections and column bases

The teaching-learning optimization (TLBO) technique is applied to unbraced steel frames with semi-rigid beam-to-column connections and semi-rigid column-to-base connections. The algorithm for design produces optimized steel frames by choosing appropriate sections from a set of standard steel sections. These standard steel sections, including wide-flange profiles (W), are provided by the American Institute of Steel Construction (AISC). The first example is subjected to the displacement, inter-story drift, and stress constraints of AISC-Load and Resistance Factor Design (LRFD) regulations. In addition, the displacement and stress limitations of the AISC-Allowable Stress Design (ASD) standard and the geometric (size) requirements are implemented in the last two examples. In finite element analysis, optimal designs of three alternative unbraced frames are performed with and without semi-rigid beam-to-column and column-to-base plate connections. All optimization techniques are encoded in the high-level programming language C# version 17.4.4 to integrate with SAP2000 version 22's Open Application Programming Interface (OAPI). The analysis results indicate that the rigidity of connections is determining parameter in the weight optimization of unbraced steel frames.

An Efficient Decoupled Reliability-Based Topology Optimization Method Based on a Performance Shift Strategy

AbstractIn this paper, a new efficient reliability-based topology optimization (RBTO) method is proposed for structures, in which the double-loop optimization is equivalently decoupled into a sequential process based on a performance shift strategy. First, a volume minimization RBTO formulation is built for structures considering displacement or compliance reliability constraints. Second, an efficient decoupling scheme is proposed to turn the double-loop RBTO into a series of deterministic topology optimization and reliability analysis. For the reliability analysis, the reliability probability is calculated based on the probability distribution function of the performance function, and the probability distribution function can be solved by the maximum entropy method based on the raw moments calculated by the multiplicative dimension reduction method. A performance shift strategy is then applied to build an equivalence between probabilistic constraint and deterministic constraint to formulate the deterministic topology optimization. Thirdly, the adjoint variable method is applied to obtain the sensitivity information for topological design variables, and a gradient-based optimization algorithm is used to update the design variables. Finally, four typical numerical examples are used to verify the advantage of the proposed method. Compared with the traditional sequential optimization and reliability assessment (SORA) method, the proposed RBTO method results in a design with a 5.4% smaller volume value to reach the same reliability index requirement for the cantilever beam, and the function calls are 354 times less than that of the SORA method.

Influences of the pile-restrained floating breakwater on extreme wave forces of coastal bridge with box-girder superstructure under the action of two-dimensional focused waves

In the complex marine environment, coastal bridges are vulnerable to damage under extreme wave action, and researchers have focused on taking effective measures to reduce structural damage and extreme wave forces in recent years. In this study, a wave-structure coupling method was utilized to numerically investigate the focused wave forces on the two-dimensional coastal bridge with a box-girder superstructure under the influence of the pile-restrained floating breakwater. After a series of validations in the focused wave generation and wave-structure interactions, the effectiveness of floating breakwaters in protecting the box-girder superstructure from extreme wave damage and the influence of control parameters of floating breakwaters on extreme wave forces were conducted. The numerical results demonstrate that the focused wave forces on the box-girder superstructure are effectively reduced after the installation of the pile-restrained floating breakwater. Compared with the floating breakwater with linear stiffness, the maximum horizontal and vertical wave forces are reduced more significantly by the floating breakwater with the displacement constraint. According to the wave parameters of the coastal bridge site, the appropriate size of the pile-restrained floating breakwater and the distance between the breakwater and the superstructure are suggested to improve the reduction effect of focused wave forces on the box-girder superstructure.

Practising “Cruel Optimism”: Eight Months on Ghazzah Street by Hilary Mantel

The essay “Practising ‘cruel optimism’: Eight Months on Ghazzah Street by Hilary Mantel” delves into Mantel’s novel through the lens of Berlant’s concept of cruel optimism. Berlant’s construct, rooted in the pursuit of conventional notions of a fulfilling existence, highlights the protagonists’ endeavors in Saudi Arabia as a postcolonial adventure bound to end in disillusionment. Mantel’s portrayal of Frances Shore and her husband Andrew illuminates the tension between their aspirations for financial security and the disconcerting realities of cultural displacement and legal constraints under Sharia law. The city’s architecture mirrors Frances’s sense of unease, resembling oppressive structures associated with fascist regimes. The portrayal of Jeddah’s construction environment, echoing totalitarian aesthetic reminiscent of fascist regimes, serves as a compelling allegory for Frances’s sense of entrapment within a society where her agency is circumscribed by gendered and legal strictures. Casting Frances as a contemporary iteration of the Gothic heroine ensnared within her domicile, Mantel explores the disjuncture between the alleged benevolence of religious doctrine and the punitive nature of its legal apparatus. Frances’s interrogation of this dissonance not only underscores the pervasive nature of cruel optimism but also hints at the inherently paradoxical nature of faith systems that simultaneously offer solace and impose constraints. Through its fluid engagement with concepts of cruel optimism, urbanity, and gender dynamics, the essay invites readers to contemplate the multifaceted interplay between individual aspiration and systemic coercion within the affluent and autocratic socio-cultural landscape.

Topology optimization with graded infill accounting for loading uncertainty

The optimal design of composite structures made of a solid phase and a given fraction of graded infill is addressed, using homogenization-based topology optimization and accounting for uncertainty in loading amplitude. A two-phase material law with void is implemented to control the amount of graded infill to be distributed, along with its admissible density range. Numerical homogenization is used to derive the macroscopic elastic properties of an isotropic and two orthotropic infills that are commonly used in additive manufacturing. A minimum weight problem is endowed with a set of deterministic displacement constraints that are equivalent to stochastic displacement enforcements in case of normal distributions of the amplitude of the applied forces. Sequential convex programming is adopted to solve the arising multi-constrained problem. Numerical simulations are performed to assess the proposed algorithm and point out peculiar features of the achieved optimal solutions with respect to layouts found in case of deterministic loads. When a fraction of graded infill is prescribed, coated structures are retrieved, whose shape may be remarkably affected by the selected type of lattice.