Displacement Constraints Research Articles

Lightweight Bus Body Design and Optimization for Rollover Crashworthiness

Lightweight design of bus body can improve energy consumption and operating cost. Nonetheless, design for strength and crashworthiness of bus superstructure is vital to occupant safety during accidents. This work proposes a methodology to design an effective lightweight frame layout and member sections of bus superstructure under requirements of bending stiffness, torsion stiffness, and rollover safety conforming to ECE-R66 based on optimization techniques. The bus configuration is firstly resolved by iterative topology optimizations with the objective function based on the structural weight and compliance subjected to the maximum displacement constraints for each load case. Topology optimization offers a preliminary design possessing the required stiffness while its structural weight is decreased by 2.5 % from the baseline model. Gauge optimization is then applied to adapt the thicknesses of the frame cross-sections. Due to high computational cost of dynamic rollover test, the correlation between nonlinear rollover test and linear quasi-static test with an adjusted deformation limit is proposed to accelerate the process. The most significant design parameter to rollover safety is shown to be the roof structure. Weight distribution and energy absorption of structural components for different models are examined and discussed as the basis to good practice in design for safety.

Meshfree-based micromechanical modelling of twill woven composites

This paper presents a novel, meshfree-based micromechanical model for homogenising the elastic properties and analysing the deformation and microscopic strains/stresses of twill woven composites. The proposed model was based on a minimum unit cell (mUC) whose internal features such as the cross-sectional shape and waviness of yarns were described by using sophisticated functions. The boundary conditions imposed on the mUC were derived by applying an equivalence approach, which converts the standard form of periodic boundary conditions into a generic set of fixed and relative displacement constraints. Theoretical formulations were developed to implement the micromechanical model within the framework of the moving kriging (MK)-based element-free Galerkin (EFG) method. An in-house computer program implementing the proposed model was developed for analysing a typical twill woven composite. Good agreements were found between the meshfree-based predictions and the reference results, highlighting the proposed model capable of homogenising twill woven composites and meanwhile avoiding the commonly required pre-processing tasks such as building an explicit geometry model and generating identical meshes on the mapping surfaces to enforce boundary conditions. Three case studies were also performed to identify the sensitivities of the predicted results to three numerical parameters, i.e. the total number of field nodes, the total number of background cells, and the support domain scaling factor. The results of these studies suggest that the numbers of field nodes and background cells used must be sufficiently large, while the support domain scaling factor in an appropriate range (e.g. 2.0−3.25) to achieve convergent results.

Reinforcement Learning and Graph Embedding for Binary Truss Topology Optimization Under Stress and Displacement Constraints

This paper addresses a combined method of reinforcement learning and graph embedding for binary topology optimization of trusses to minimize total structural volume under stress and displacement constraints. Although conventional deep learning methods owe their success to a convolutional neural network that is capable of capturing higher level latent information from pixels, the convolution is difficult to apply to discrete structures due to their irregular connectivity. Instead, a method based on graph embedding is proposed here to extract the features of bar members. This way, all the members have a feature vector with the same size representing their neighbor information such as connectivity and force flows from the loaded nodes to the supports. The features are used to implement reinforcement learning where an action taker called agent is trained to sequentially eliminate unnecessary members from Level-1 ground structure, where all neighboring nodes are connected by members. The trained agent is capable of finding sub-optimal solutions at a low computational cost, and it is reusable to other trusses with different geometry, topology and boundary conditions.

Fabrication, Experiment, and Simulation of a Flexible Microvalve-Integrated Microarm for Microgrippers Using Electrorheological Fluid

Because of the power density advantages of fluid power systems, many researchers have developed microactuators using homogeneous electrorheological (ER) fluids (ERFs) for applications to various micromachines. An ER valve, as a critical component of the ER actuator, can control ERF flow by the apparent viscosity increase resulting from the applied electric field without any mechanical moving parts. Hence, it is adequate for the miniaturization of a fluidic microactuator. However, it is not easy to integrate rigid ER valves into soft microrobots. To overcome these limitations, we developed a novel elastic ER microarm using flexible ER valves (FERVs) in this study. Each microarm consists of an FERV, a movable chamber, and a displacement constraint element, so that it bends with the inner pressure controlled by the FERV. We proposed and developed a micro-electromechanical system fabrication process for the FERV, movable chamber, and displacement constraint element. By utilizing the proposed method, we successfully fabricate a FERV-integrated microarm. The characteristics of the FERV were experimentally clarified. In addition, the bending motion of the FERV-integrated microarm was demonstrated by experiments and verified by finite-element method simulation. This ER microarm was shown to be feasible for an ER microgripper composed of multiple microarms.

Theoretical research into cyclic web buckling and plastic overstrength of shear links

In this paper, a numerical model for shear links was firstly established and carefully validated, and the cyclic web buckling behavior were also discussed with comparison to experimental results. On this basis, firstly, the influence of boundary conditions was explored. The influence of axial displacement constraint on cyclic buckling and plastic overstrength was discussed, and a theoretical plastic overstrength factor considering axial displacement constraint was proposed. In addition, the influence of axial forces on cyclic buckling and plastic overstrength was discussed, and the limited range of axial forces on shear links was recommended. Afterwards, the influence of various parameters on cyclic web buckling was analyzed and discussed, and a theoretical prediction approach for cyclic buckling angle was proposed, which was applicable to shear links with or without stiffeners. Also, the influence of parameters on plastic overstrength was analyzed and discussed, and the theoretical model of the relationship between plastic overstrength and displacement angle was proposed for shear links with or without stiffeners. Finally, based on the works above, a simplified theoretical model to predict the relationship between shear force and displacement angle was proposed, with consideration of cyclic buckling. The experimental validations confirmed it had good accuracy. • The influence of axial boundary conditions on cyclic web buckling and plastic overstrength of shear links was discussed. • The cyclic web buckling was parametrically studied, and a theoretical approach predicting buckling angle was given. • The plastic overstrength was parametrically studied, and a theoretical prediction approach was given. • The theoretical prediction model for skeleton curve of shear links was proposed, which gave good prediction results.

Height Growth in Layered Unconventional Reservoirs: The Impact of Formation Moduli, Interfaces, and In-Situ Stress

Summary In recent years, much research effort has focused on hydraulic fracture (HF) height growth because height containment is needed to ensure effective stimulation of target zones. In many cases, fracture height growth determines the success or failure of a hydraulic stimulation. For layered rock systems, material properties, interface mechanical characteristics and permeability, and in-situ stresses influence both the lateral and height growth of HFs. It is generally believed that stress contrast is a dominant factor that directly controls the fracture height. The influence of Young's modulus contrast on height growth is usually ignored. Simplified “average methods” are often proposed and used to homogenize layered modulus. Also, it is commonly assumed that the layer interfaces are perfectly bonded without slippage even when high stress contrast exits. The above assumptions are made partially due to the difficulty in handling all the factors (e.g., layered modulus and stress contrast between adjacent layers) involved in simulations. In this study, a fully coupled 3D HF simulator that is based on the finite element method (FEM) is used to investigate the above factors and study how they impact HF propagation and height growth. The influence of modulus contrast, interface conditions, and in-situ stress on hydraulic fracturing and especially on fracture height growth is analyzed. The numerical approach is a 3D FEM with a special zero-thickness interface element based on the cohesive zone model (CZM) to simulate the fracture propagation and fluid flow in fractures. A local traction-separation law with strain-softening is used to capture tensile cracking. The nonlinear mechanical behavior of frictional sliding along interface surfaces is also considered. Because discontinuities are explicitly simulated through using the interface elements, details of the deformation processes are captured and revealed. For example, information related to aperture opening/sliding and stress distribution along the discontinuities is obtained in the simulations. After verification and validation of the numerical model, it is used to simulate height growth in layered rock of practical interest. The numerical model is evaluated through a commonly used crossing/arrest criterion. Laboratory experiments on fracture-discontinuity interaction under triaxial stress conditions are also studied. Numerical results match well with predictions from theoretical formulations and with laboratory observations. Typical processes associated with fracture-discontinuity interaction are revealed. The recorded injection pressure increases when the HF reaches a bedding interface (or other discontinuities). Continuous opening and/or sliding along the interface requires higher injection pressure. With the existence of a horizontal interface, the influence of modulus contrast and stress contrast on HF height growth is analyzed. The combined effects of rock properties, mechanical properties of the interfaces, and in-situ stress can effectively inhibit HF height growth. Analyzing pressure and aperture responses during fracture/interface interaction, it is revealed that the injection net pressure in the case where an offset exists along the interface is larger than that required if the HF could propagate continuously across the interface (no offset from the intersection point to the flaw along the interface). Whenever the free propagation of fracture tips is limited, either by horizontal formation interface or displacement constraints set intentionally to prevent fracture propagation, the injection net pressure and aperture at the injection point exhibit increase.

An efficient SPH methodology for modelling mechanical characteristics of particulate composites

Particulate composites are one of the widely used materials in producing numerous state-of-the-art components in biomedical, automobile, aerospace including defence technology. Variety of modelling techniques have been adopted in the past to model mechanical behaviour of particulate composites. Due to their favourable properties, particle-based methods provide a convenient platform to model failure or fracture of these composites. Smooth particle hydrodynamics (SPH) is one of such methods which demonstrate excellent potential for modelling failure or fracture of particulate composites in a Lagrangian setting. One of the major challenges in using SPH method for modelling composite materials depends on accurate and efficient way to treat interface and boundary conditions. In this paper, a master-slave method based multi-freedom constraints is proposed to impose essential boundary conditions and interfacial displacement constraints in modelling mechanical behaviour of composite materials using SPH method. The proposed methodology enforces the above constraints more accurately and requires only smaller condition number for system stiffness matrix than the procedures based on typical penalty function approach. A minimum cut-off value-based error criteria is employed to improve the computational efficiency of the proposed methodology. In addition, the proposed method is further enhanced by adopting a modified numerical interpolation scheme along the boundary to increase the accuracy and computational efficiency. The numerical examples demonstrate that the proposed master-slave approach yields better accuracy in enforcing displacement constraints and requires approximately the same computational time as that of penalty method.

Neural networks-based adaptive dynamic surface control for vehicle active suspension systems with time-varying displacement constraints

This paper addresses controlling of displacements of vehicle active suspension systems with an active seat suspension and a human-body model. A neural networks-based dynamic surface control strategy is constructed for the active suspension systems. Specifically, asymmetric time-varying barrier Lyapunov functions are applied to ensure that the displacements of vehicle active suspensions do not violate their time-varying constraint bounds. Neural networks are used to approximate unknown functions in the active suspension systems and their basis function properties are employed to deal with functions with non-strict form. Dynamic surface control technique is used to reduce the complexity of the controller. Advantages of the control strategy are substantiated by two simulation examples.

Prebuckling and buckling analysis of moderately thick variable angle tow composite plates considering the extension-shear coupling

In this paper, an analytical model based on a generalized Rayleigh-Ritz method is developed to deal with both the prebuckling and buckling problems of moderately thick VAT composite plates under a more general in-plane boundary condition. The non-uniform in-plane stress fields of VAT composite plates under various in-plane boundary conditions is firstly determined based on the minimum complementary energy principle combined with the Airy’s stress function. Afterwards, the governing equation of buckling problem of VAT composite plates under non-uniform in-plane stress fields is derived based on third-order shear deformation theory of Reddy’s type. The innovation of this paper lies in that a linear fitting method combined with Chebyshev-Gauss-Labotto point distribution is introduced to retrieve the boundary stress coefficients from the stress constraint conditions generated by the Lagrangian multiplier method, and meanwhile an integral expression of work done by the unknown boundary force along the prescribed in-plane displacement is adopted to satisfy the displacement constraint condition along the boundary line. In so doing, three kinds of in-plane boundary conditions are taken into account, that is, pure stress boundary condition, pure displacement boundary condition and mixed stress and displacement boundary condition. In addition, no assumption is made on the extension-shear coupling terms and thus the proposed analytical model is suitable to the unbalanced layup. The accuracy and robustness of the proposed analytical model is validated by finite element analysis and with prior results. Effects of the in-plane boundary condition, extension-shear coupling and varying fibre orientation angles on both in-plane stress and buckling responses of VAT composite plates are studied by numerical examples. It is shown that for the balanced panels under uniform compression, the benign load redistribution mechanism offered by the VAT layups remain in effect even if there exists the non-uniform shear constraint along the loading edges. However, the buckling load of the panel can be reduced by the shear constraint along the loading edges to a certain degree. Furthermore, it is found that for some displacement-controlled shear loading cases, the extension-shear coupling plays a positive role in the load redistribution, which results in a sight improvement in the longitudinal load of the panel when critical buckling occurs.

Topological Optimization Methods in the 3D Printer Software Package

The software for the topological optimization of parts with different constraints of the objective function, as well as for the generation and use of different types of lattice structures for filling the parts, is developed within the project Development of the Atlas of Standard Forms for Topological Optimization of Structures Formed by Selective Laser Melting and Their Production Verification (agreement with the Ministry of Education and Science, project no. 2016-14-579-0009-492) carried out by the National University of Science and Technology MISiS, State Scientific Center of the Russian Federation AO NPO CNIITMASH, the All-Russian Scientific Research Institute of Experimental Physics, the Ministry of Education and Science of the Russian Federation, and OAO Nauka i innovatsii (State Atomic Energy Corporation Rosatom). The article describes the methods and algorithms of topological optimization of structures with the displacement and stress constraints of the objective function developed for the basic version of the software.

Adptive Multi-scale Finite Element Considering Local Buckling of Members for Latticed Frames

To consider the local buckling of the members in the reticulated frames, based on the multi-scale simulation, the part of member that having local buckling is divided by the shell elements as a micro-model, and the other part of the member was simulated by beam elements as a macro-model. The incremental displacement constraint equations for the nodes on the section between the two models are established based on the plane section premise of classical beam theory. A method to introduce the constraint equations is derived based on the Updated Largrangian method. The location of the micro-model is predicted by the deflection function of the beam, and the length of the collapsed part is estimated. Its accuracy proves to be satisfied by the pure shell element model.

Influence of displacement constraints to the surface reconstruction of stressed bicrystal thin films

In this work, surface morphology evolution of bicrystal thin films under the combined action of grain boundary and surface diffusion is investigated by considering different mechanical constraints. 2D surface topographies of thin films, that are (a) freestanding, (b) strongly bonded to its substrate and (c) strongly bonded to its substrate and one of sidewalls, are simulated using a numerical implementation of an irreversible thermo-kinetics model. Relationships which give the groove depth as a function of time are obtained. Results show that mechanical loading conditions are effective in determining the morphology and kinetics of grooving. For the three scenarios that had been investigated, it was found that the groove depth evolves linearly with different tip velocities under the same level of uniaxial tension. In freestanding films groove tip evolves faster; i.e. as the film gets constrained from its substrate and/or one of its sidewalls, the tip velocity slows down. It was also observed that high triple junction mobilities at low levels of applied stress hinder the effects of displacement constraints to groove shape, even in the case of asymmetric stress distributions inside the film. On the other hand, low triple junction mobilities at moderate applied stresses allow formation of asymmetric grain boundary grooves due to the induced asymmetry in the driving force for surface diffusion with respect to the grain boundary.

A novel approach for the rigid body guidance synthesis of planar RRPR linkages

This paper demonstrates that the maximum number of poses that can be exactly reached by a planar RRPR linkage is four, while the design for five poses requires the relaxation of displacement constraints at one prescribed pose. To this end, a novel and explicit condition for the synthesis of RP dyads with five prescribed poses is correspondingly introduced. It leads to a new and efficient approach to synthesize planar RRPR linkages, which is equipped with a branching identification procedure. Two successful case studies are provided to validate the applicability of the proposed synthesis approach.

Multi-scale Finite Element Method for Members for Pipe Frames

To consider the local buckling of the members in reticulated frames, based on the multi-scale simulation, the part of member may be collapsed were divided by the shell elements as a micro-model, and the other part of the member was simulated by beam elements as a macro-model. The incremental displacement constraint equations for the nodes on the section between the two models are established based on the plane section premise of classical beam theory. By constraint variational principle, the tangent stiffness matrixes and the nodal load vectors of the micro-model and the outside structure are combined, and then the equations are solved. The location of the collapsed part is predicted by the deflection function of the beam, and the length of the collapsed part is estimated. Two case studies about a single beam and a single-layer reticulated dome are presented to show the feasibility and the validity of this method.

Bi-directional Evolutionary Structural Optimization of Continuum Structures with Multiple Constraints

Most of the structural topology optimization problems involved in practical engineering applications are problems with many constraints. Thus, this paper presented an improved bi-directional evolutionary structural optimization (BESO) method for problems with many constraints. Slack variables were introduced to transform the inequality constraints into equality constraints. Then the Lagrange multiplier method converted the multi-constrained optimization problem to an unconstrained optimization problem and an advanced multiplier calculation was proposed. Elemental sensitivity numbers were derived according to the obtained multipliers. The design variables were updated by the BESO method. One numerical example that aimed to minimizing the structural mean compliance and involved volume, fundamental frequency and displacement constraints was used to validate the proposed method. The new method extends the BESO method to topology optimization that has a number of constraints, such as volume, displacement and frequency constraints.

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

This paper studies topology optimisation problems of truss structures under non-stationary random seismic excitations considering displacement and stress constraints. The optimisation model of truss structures is formulated by taking volume minimisation with constraints on variances of displacements and stresses. The explicit time domain method (ETDM) is applied to analyse the stochastic responses of the structure and the sensitivities with respect to the design variables. Based on the sensitivity analysis, the nodal positions and the cross-sectional areas of the bar elements of the truss structures are optimised simultaneously by using the globally convergent method of moving asymptotes (GCMMA). Meanwhile, a scheme is proposed to delete zero bars and redundant nodes during the optimisation process. Finally, several topology optimisation examples of 2-D and 3-D truss structures illustrate the accuracy and computational efficiency of the proposed method.

Topology optimization of shear wall structures under seismic loading

A topology optimization formulation is developed to find the stiffest structure with desirable material distribution subjected to seismic loads. Finite element models of the structures are generated and the optimality criteria method is modified using a simple penalty approach and introducing fictitious strain energy to simultaneously consider both material volume and displacement constraints. Different types of shear walls with/without opening are investigated. Additionally, the effects of shear wall-frame interaction for single and coupled shear walls are studied. Gravity and seismic loads are applied to the shear walls so that the definitions provide a practical approach for locating the critical parts of these structures. The results suggest new viewpoints for architectural and structural engineering for placement of openings.

Buckling of piezoelectric sandwich microplates with arbitrary in-plane BCs rested on foundation: effect of hygro-thermo-electro-elastic field

Buckling and post-buckling behaviors of simply supported microplates in complex environment are studied, where elastic foundation and hygro-thermal-electro-mechanical loads are considered. The first-order shear deformation theory is used to establish basic equations of the microplate considering the von Karman’s nonlinearity. The size-dependent effect is characterized by the modified couple stress theory. A unified boundary condition model is introduced to discuss various in-plane boundary conditions (BCs). Analytical solutions for critical mechanical/hygrothermal buckling loads and post-buckling paths of the microplate under different in-plane BCs are obtained by using the perturbation method and the Galerkin method, respectively. Results reveal that size-dependent effect and elastic foundation enhance the stiffness of the microplate. Transverse displacement of the microplate in the post-buckling stage increases with the external compressive load, temperature and moisture concentration, expressing a nonlinear curve. When the displacement constraint in the normal direction is applied on the microplate edge, the critical mechanical/hygrothermal buckling load decreases. These results can be utilized in the optimization design of the micro-electro-mechanical systems.

A First Step Towards the Numerical Simulation of the Forming of flat TFP Preforms

The mechanical efficiency of fiber-reinforced composite materials mainly depends on the alignment of fibers along the load paths arising from the boundary conditions applied to the part. On this basis, the Tailored Fiber Placement (TFP) consists in building a fibrous reinforcement by continuously laying down a tow on a plane backing material which can be a polymer film or a fibrous reinforcement such as woven fabrics or NCF. The tows are maintained in place with the desired orientation with a stitch. To fully take advantage of the design freedom offered by TFP in composite stamping, the designer who can compute the optimized fiber orientations in the final 3D part, has still to determine the tow’s path on the plane backing material since tow’s motions will inevitably occur during the forming process. The present study which falls within the simulation of material forming attempts to model the behavior of TFP preforms using the finite elements method. The backing material is represented by a mesh of 2D elements with embedded linear beam element modeling explicitly the tow’s layout analogously to the modeling of reinforced concrete in civil engineering applications. Consequently the degrees of freedom of the beams are interpolated from the host element. However the displacement constraint at the beam nodes is relaxed in the tow’s path direction. To demonstrate the accuracy of this finite element formulation, standard tests for fiber-reinforced composites such as bias extension test as well as a simple 3D test case will be presented.

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.