Displacement Constraints Research Articles

3-D Distributed Localization With Mixed Local Relative Measurements

This paper studies 3-D distributed network localization using mixed types of local relative measurements. Each node holds a local coordinate frame without a common orientation and can only measure one type of information (relative position, distance, relative bearing, angle, or ratio-of-distance measurements) about its neighboring nodes in its local coordinate frame. A novel rigidity-theory-based distributed localization is developed to overcome the challenge due to the absence of a global coordinate frame. The main idea is to construct displacement constraints for the positions of the nodes by using mixed local relative measurements. Then, a linear distributed localization algorithm is proposed for each free node to estimate its position by solving the displacement constraints. The algebraic condition and graph condition are obtained to guarantee the global convergence of the proposed distributed localization algorithm.

Feature-Integrated Structural Optimization Design Method and Performance Evaluation for Hollow Slab Structures

In view of the main contradiction between traditional topology optimization for basic theory research and the actual requirements of comprehensive performance for modern industrial products, a feature-integrated structural optimization design method with an appropriate reliability, a light weight, and excellent mechanical properties for continuum structures was established based on the reliability-based topology optimization of modified minimum weight with a displacement constraint (RBTO-MMWDC) model. Taking hollow slab structures as an example, a graphical user interface based on the optimization code was developed for practical applications. Furthermore, the topological layout of $\beta =3.0$ was selected for geometric model reconstruction and mechanical property evaluations were performed using the finite element method (FEM) and experiments. Compared with those of the traditional structure, the compression resistance and bending resistance properties of the optimized structure are improved by 29% and 75%, respectively, and the first-order natural frequency is increased by 101%. In addition, the results of the experiments are consistent with the simulation in terms of tendency. The bending resistance strength and stiffness of the optimized structure are improved by 61% and 55%, respectively. This study provides a theoretical reference and feasible solution for the feature-integrated design of continuum structures in engineering applications.

Topology optimisation of truss structures under non-stationary random seismic excitations with displacement and stress constraints

Topology optimisation of truss structures under non-stationary random seismic excitations with displacement and stress constraints

Adaptive Fault Tolerant Control of Active Suspension Systems With Time-Varying Displacement and Velocity Constraints

In this paper, active suspension system is selected as the research object. Back-stepping method is adopted, and virtual fault tolerant controller, main fault tolerant controller and adaptive law are designed by constructing Time-varying Barrier Lyapunov Function (TVBLF), to ensure that the displacement and speed of the vehicle do not violate the constraint boundary and achieve the goal of fast fault tolerance. For the unknown continuous function caused by the uncertain body mass and other factors in the system, Radial Basis Function Neural Network (RBFNN) is used for approximation. At the same time, the suspension space limitation and tire dynamic load are analyzed. Finally, the effectiveness of the proposed fault-tolerant control method is verified by simulation of deviation fault and partial failure fault.

A research on optimum designs of steel frames including soil effects or semi rigid supports using Jaya algorithm

The effect of soil foundation plays active role in optimum design of steel space frames when included. However, its influence on design can be calculated after a long iterative procedure. So it requires longer computer time and more computational effort if it is done properly. The main purpose of this study is to investigate how these effects can be calculated in more practical way in a shorter time. The effects of semi-rigid column bases are taken into account in optimum design of steel space frames. This study is carried out by using JAYA algorithm which is a novel and practical method based on a single revision equation. The displacement, stress and geometric size constraints are considered in the optimum design. A computer program is coded in MATLAB to achieve corporation with SAP2000-OAPI (Open Application Programming Interface) for optimum solutions. Four different steel space frames including soil structure interaction taken from literature are investigated according to different semi-rigidly supported models depending on different rotational stiffness values. And the results obtained from analyses are compared with the results available in reference studies. The results of the study show that semi-rigidly supported systems in the range of appropriate rotational stiffness values offer practical solutions in a very short time. And close agreement is obtained with the studies on optimum design of steel space frames including soil effect underneath.

Topology optimization of structures considering local material uncertainties in additive manufacturing

Additive manufacturing provides more freedom for the design of structures but also exhibits prominent local uncertainties of material properties, which bring potential challenges. The performance of structures should depend not only on uncertain variations of material properties but also on the spatial occurrence frequency of the extreme material properties. This paper proposes a non-probabilistic reliability-based topology optimization algorithm by considering local material uncertainties in additive manufacturing. The whole design domain is divided into several uncertainty regions (URs), whose size is proportional to the spatial occurrence frequency of extreme material properties. Within each UR, these uncertain-but-bounded variations of materials are correlated by the multi-dimensional ellipsoid model. Then, the multi-ellipsoid model for all URs is established by considering the overall material uncertainties of the structure. Thereafter, a non-probabilistic reliability-based topology optimization (NRBTO) is proposed for minimizing structural volume against displacement constraints by considering material uncertainties during additive manufacturing. Several 2D and 3D examples are presented to illustrate the effectiveness of the proposed method. Compared with solutions resulting from the deterministic topology optimization (DTO), NRBTO provides conservative designs with a larger volume fraction due to material uncertainties. When smaller URs are assigned to indicate the high occurrence frequency of extreme material properties, the NRBTO design becomes even conservative. The extreme case is equivalent to the deterministic topology optimization using the lower bound material.

Lightweight topology optimization with consideration of the fail-safe design principle for continuum structures

ABSTRACT The topology optimization of continuum structures is investigated to obtain an optimized topology satisfying the fail-safe design principle with suitable redundancy components. An optimization model with a nonlinear objective and linear constraints is established by defining the reciprocal topology variable as design variables and linearly approximating the structural performance. The model is solved by a dual sequential quadratic programming (DSQP) algorithm. Topology optimization with displacement constraints is used as an example. The presented optimization model and solution approach offers the following advantages. (1) A volume constraint, which makes determining reasonable values difficult, need not be specified. (2) Weighted coefficients, which combine multiple compliances under different load cases into a combined compliance, need not be specified as well. (3) The presented optimization model is a type of single-objective programming and thus avoids the challenges in the min-max model. (4) The proposed method shows a strong capability of finding optimum solutions.

Design optimization of semi-rigid plane steel frames with semi-rigid bases using biogeography-based optimization and genetic algorithms

This paper performs optimization for plane steel frames with semi-rigid beam-to-column connections, in a company with fixed, semi-rigid and hinged base connections using a biogeography-based optimization algorithm (BBO), along with a genetic algorithm (GA). In this paper, Kanvinde and Grilli [1] nonlinear model is used for simulating semi-rigid base connections, where this model considers all deformations in different base connection components under the applied loads to determine the relative spring rotation for the sake of getting accurate base rotational stiffness value. In addition, Frye and Morris [2] nonlinear model is used for simulating semi-rigid beam-to-column connections. The P-∆ effect and geometric nonlinearity are considered. The stress and displacement constraints of AISC-LRFD [3] specifications, together with size adjustment constraints, are considered in the design procedure.

An experimental approach to evaluating the long-term performance of segmental linings

There have been numerous engineering projects involving shallow buried metro tunnels underneath the subgrade of high-speed railways in China, and the metro tunnel inevitably bears the dynamic load induced by the high-speed trains above. Thus, the long-term performance of segmental linings cannot be negligible. An experimental model is an important method for evaluating the segmental linings. In the experiment, three key problems must be solved to ensure the strict similarity between the prototype and the model in terms of the structural form, initial earth pressure and fatigue behaviour of the segmental linings. A series of key points to maintain the similarity of the model is put forward, including the presentation of the standard joint-staggered model, the principle of a reserved displacement constraint device and the equivalence of fatigue life between the prototype and model materials. Based on similarity theory, a 1/10-scale model experiment is designed, and the stress and strain states are measured. The results show the model experimental design can be approximately consistent with the theoretical calculation and numerical simulation. The study provides a sufficient experimental basis for evaluating the long-term performance of segmental linings.

Lightweight design of electric bus roof structure using multi-material topology optimisation

This paper presents a multi-material topology optimisation (MMTO) process for the lightweight design of an electric bus roof structure including the self-weight. The usage of electric buses is increasing owing to environmental issues. However, it is challenging to design a lightweight structure, because the heavy battery pack mounted on the roof increases the deformation and reduces the safety. In a design including the self-weight, the appropriate distribution of multiple materials improves the performance more than that of a single material. The MMTO method has been applied to identify the optimal distribution of multiple materials. However, in the real-engineering problem, only a simple objective function such as compliance and a single constraint function such as the volume of material have been considered, whereas the mass reduction is the most important factor. In this paper, an MMTO process is proposed for the lightweight design of the bus roof structure to consider multiple displacement constraints including the self-weight. To control the complexity of the distribution of multiple materials for improving the manufacturability, the welding surface function is proposed. An optimisation process was constructed that can handle the complex finite-element model and multiple load cases, and it was validated according to the well-known compliance minimisation problem. Mass reduction was achieved via the lightweight optimisation, and the interfacial area between the different materials was reduced by employing the welding surface function.

Adaptive Neural Network Control for Active Suspension Systems With Time-Varying Vertical Displacement and Speed Constraints

In this paper, an adaptive neural network (NN) control scheme is proposed for a quarter-car model, which is the active suspension system (ASS) with the time-varying vertical displacement and speed constraints and unknown mass of car body. The NNs are used to approximate the unknown mass of car body. It is commonly known that the stability and security of the ASSs will be weakened when the constraints are violated. Thus, the control problem of the time-varying vertical displacement and speed constraints for the quarter-car ASSs is a very important task because of the demand of the handing safety. The time-varying barrier Lyapunov functions are used to guarantee the constraints of the vertical displacement not violated, and it can prove the stability of the closed-loop system. Finally, a simulation example for the ASSs is employed to show the feasibility and rationality of the proposed approach.

On the mechanics of thermal buckling of oil storage tanks

Abstract This paper addresses the thermal buckling behavior of tanks having a fixed roof, as employed to store fuel in the oil industry. The study is performed based on finite element analyses of the shell, including linear analysis, linear bifurcation analysis, and geometrically and constitutive nonlinear analysis, in order to elucidate the mechanics of stress redistribution at pre-buckling and buckling states. Based on previous works, the roof is modeled as a conical shell with an equivalent uniform thickness. The results show that the stress field due to a uniform temperature around the circumference is considerably different from that obtained for a non-uniform field as modeled in cases of temperatures due to an adjacent fire: Under uniform temperatures around the circumference the shell does not provide vertical restrain and buckling is dominated by hoop action; whereas displacement constraints are present under a non-uniform temperature, leading to buckling dominated by meridional stresses. Contrary to what has been suggested, the tank under uniform temperature cannot be taken as an upper bound to the buckling of a tank under an adjacent fire. In the evaluation of critical temperatures, the influence of geometric relations H/D (height to diameter) and R/t (radius to thickness) are independent of each other. It is shown that the problem is not imperfection-sensitive. Finally, thermal buckling mode and critical temperatures are strongly dependent on the H/D ratio of the cylindrical shell.

A novel scheme for imposing periodic boundary conditions on RVE in second-order computational homogenization for granular material

Purpose This paper aims to present a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the representative volume element (RVE) of discrete particle assembly in the frame of the second-order computational homogenization methods for granular materials. Design/methodology/approach The proposed scheme is based on the generalized Hill’s lemma of gradient Cosserat continuum and the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE of discrete particle assembly. The generalized Hill’s lemma conducts to downscale the macroscopic strain or stress measures and to impose the periodic boundary conditions on the RVE boundary so that the Hill-Mandel energy equivalence condition is ensured. Because of the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE, the periodic boundary displacement and traction constraints together with the downscaled macroscopic strains and strain gradients, micro-rotations and curvatures are imposed in the point-wise sense without the need of introducing the Lagrange multipliers for enforcing the periodic boundary displacement and traction constraints in a weak sense. Findings Numerical results demonstrate that the applicability and effectiveness of the proposed scheme in imposing the periodic boundary conditions on the RVE. The results of the RVE subjected to the periodic boundary conditions together with the displacement boundary conditions in the second-order computational homogenization for granular materials provide the desired estimations, which lie between the upper and the lower bounds provided by the displacement and the traction boundary conditions imposed on the RVE respectively. Research limitations/implications Each grain in the particulate system under consideration is assumed to be rigid and circular. Practical implications The proposed scheme for imposing periodic boundary conditions on the RVE can be adopted solely for estimating the effective mechanical properties of granular materials and/or integrated into the frame of the second-order computational homogenization method with a nested finite element method-discrete element method solution procedure for granular materials. It will tend to provide, at least theoretically, more reasonable results for effective material properties and solutions of a macroscopic boundary value problem simulated by the computational homogenization method. Originality/value This paper presents a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the RVE of discrete particle assembly for granular materials without need of introducing Lagrange multipliers for enforcing periodic boundary conditions in a weak (integration) sense.

Critical Evaluation of Metaheuristic Algorithms for Weight Minimization of Truss Structures

This study critically compares variants of Genetic Algorithms, Particle Swarm Optimization, Artificial Bee Colony, Differential Evolution and Simulated Annealing used in truss sizing optimization problems including displacement and stress constraints. The comparison is based on several benchmark problems of varying complexity number of design variables. i.e. the number of design variables, and the degree of static indeterminacy. Most of these problems have been studied by numerous researchers using a large variety of methods; this allows for absolute rather than relative comparison. Rigorous statistical analysis based on large sample size, as well as monitoring of the success rate throughout the optimization process, reveal and explain the convergence behavior observed for each method. The results indicate that, for the problem at hand, Differential Evolution is the best algorithm in terms of robustness, performance, and scalability.

Combined peridynamic and finite element analyses for failure prediction in periodic and partially periodic perforated structures

This study presents an approach for predicting the displacement and stress fields in fully-periodic or partially-periodic perforated structures. The distance between the cells of perforation can be thick or thin with or without an outer frame. Employing the concepts from micromechanics and mechanics of structural genome, a perforated structure can be modeled as an imperforated structure by employing traditional finite elements with effective material properties. The effective material property matrix is determined by applying the peridynamic unit cell (PDUC) model to the repeating perforation (cell). The prediction of stress field and failure process in the unit cell referred to as “dehomogenization’ is achieved by constructing its PD model subjected to displacement constraints from the analysis of imperforated structure. Both the PD and FE analyses are performed by employing only the built-in elements of a commercial finite element software, ANSYS. After demonstrating the computational framework and verifying the predictions, a complex partially-perforated circular glass filter is modeled for the stress field and failure characteristics. Although the glass filters are commonly two-dimensional in nature, the present approach is suitable for three-dimensional analysis of structures with a periodic architecture.

Upgrade and development of elastic surface inverse design method for axial compressor cascade with sharp-edged blades

The aim of an inverse design method is to calculate the geometry corresponding to a target pressure distribution along the walls. Elastic Surface Algorithm (ESA), as one of the newest residual-corrective inverse design method, was proposed for external flows in 2014. In this method, the airfoil walls were considered as a flexible elastic beam that deforms due to the difference between the target and current pressure distribution at each shape modification step. Nevertheless, the previous version of ESA is subjected to oscillation, instability, and divergence for a cascade of sharp-edged blades due to the steep pressure gradient at the leading edge. This study upgrades the ESA for the shape design of sharp-edged blades with steep gradients of pressure near the stagnation point. The basis of this upgrade was to use the deflection curve of Timoshenko beam which is continuous and differentiable at all the nodes. The upgraded ESA against the original ESA used only the physical characteristics of Timoshenko beam instead of applying a geometric filtration for the removal of fractures in the intermediate profiles at large deformations. To increase the beam deformation at each shape modification, the upgraded ESA removed the constraint of node displacement along the spine direction, which is normal to the chord line, so that the nodes of Timoshenko beam could freely move based on the large deformation equations. In addition, the optimal values of elastic modulus, thickness, and width of the beam were obtained to increase the convergence rate of the ESA. The upgraded ESA was finally verified for a DCA blade cascade in subsonic and transonic flow regimes under different angles of attack and different initially-guessed geometries. The results showed the upgraded ESA to be a robust, flexible, and fast-converging inverse design method for sharp-edged blades with steep pressure gradients.

Optimal Design of Steel Curved Roof Frames by Enhanced Vibrating Particles System Algorithm

The paper presents an optimal design of steel curved roof frames with its roof being part of a circular arc. The elements of frames are tapered I-section members. In the objective function for optimization, two factors affecting the weight of frames are considered simultaneously. First, the roof slope angle as an effective variable on the values of the structural loading and second, the cross-section of members that are considered as continuous and discrete variables, respectively. In the range of 3 to 70 degrees, the optimum range of roof slope angles for steel curved roof frames, as well as precise value of the best roof slope angle, will be reported. Enhanced Vibrating Particles System (EVPS) algorithm is utilized for the optimal design of steel curved roof frames with tapered members. The performance and efficiency of the EVPS algorithm is compared with six other recently developed optimization algorithms including VPS, GWO, HS, SSA, ECBO and GOA algorithms. The effectiveness and performance of EVPS algorithm is proven. Frames design are performed using ANSI/AISC 360-05 specifications which strength, displacement and stability constraints are imposed on the frames.

Micromechanical modeling of unidirectional composites with random fiber and interphase thickness distributions

Unidirectional composites having random fiber and interphase thickness distributions are considered, and the corresponding transverse effective mechanical properties are determined by the computational homogenization method developed based on linear elastic equilibrium relationship in multi-phase composite. The micromechanical unit cell model including random coated fibers is generated by a simple and efficient algorithm, and the periodic displacement constraints are applied on the cell boundary to keep the cell edges straight after deformation. Then, the effective transverse elastic properties of composites are determined numerically by the present computational model, which is validated through a comparison against available experimental and analytical/numerical results. Finally, the influences of micromechanical parameters on composites are investigated. It is observed that the nonuniformity of interphase thickness has little influence to the overall material properties of composites, which are significantly affected by the interphase thickness and elastic modulus, especially for the case of high fiber volume content.

The lightweight topology optimization of multi-material structures with displacement constraints

Multi-material Topology Optimization is a simulation technique based on the principle of the finite element method which is able to determine the optimal distribution of two or more different materials in combination under thermal and mechanical loads. This paper develops a lightweight topology optimization formulation of multi-material structures considering displacement constraints based on independent, continuous and mapping (ICM) method. Furthermore, explicit expression of optimised formulation is derived, approximations of displacement and weight are given by the first and second order Taylor expansion. And the optimization problem is solved by sequential quadratic programming approach. The feasibility and effectiveness of proposed method are demonstrated by numerical examples. It is found that the best transfer path of load is provided using multi-material topology optimization. The results show that a clear topological structure is obtained and the best transfer path of load is provided after multi-material topology optimization. In addition, under the precondition of satisfying the displacement constraint condition, the weight of the optimized structure based on various materials is lighter. The weight of multi-material topology optimization structure decreases with the increase of displacement constraint. And the optimal topological structure of the multi-material is different with the component materials. Besides, the optimization model established by using the structural performance parameters as a constraint is more reliable and more suitable for practical engineering applications.

Instability-Triggered Triply Negative Mechanical Metamaterial

We report a three-dimensional mechanical metamaterial that simultaneously possesses negative stiffness, negative bulk modulus, and negative Poisson's ratio. This metamaterial is a periodic arrangement of binder-shell elements. Under compression, the spherical shells dent inwards which cause the material to contract in the lateral directions. At larger deformations, snap through instability occurs and the material exhibits negative incremental stiffness. Interestingly, both incremental stiffness and incremental Poisson's ratio approach negative infinity (under displacement control) when snap-back is observed. We further showed that the multi-negative index metamaterial satisfies the strong ellipticity condition, therefore, a block of the metamaterial with many unit cells is stable under displacement constraint.