Nodal Displacements Research Articles

Optimization of truss structures using multi-objective cheetah optimizer

In this study, a multi-objective version of the recently proposed cheetah optimizer called multi-objective cheetah optimizer (MOCO) has been proposed. MOCO draws inspiration from the targeted hunting strategy employed by cheetahs, which involves a sequence of actions: searching for prey, patiently waiting for the right moment to attack, swiftly launching the attack, and then retreating from the prey and returning to their habitat. MOCO is the result of modification and enhancement from its single-objective counterpart, utilizing a Pareto dominance-based approach. This adaptation allows MOCO to efficiently handle multiple objectives, explores and exploits promising areas in the optimization landscape, and identifies non-dominated solutions, offering valuable tradeoff choices for decision-makers. To demonstrate its practical applications, the MOCO method has been employed to address five intricate structural design problems. These problems involve a pair of competing objectives: the minimization of structural weight and the reduction of maximum nodal displacement. To gauge the efficacy and efficiency of the proposed algorithm, a comparative analysis is conducted against three alternative state-of-the-art multi-objective algorithms. Furthermore, a rigorous evaluation is carried out utilizing hypervolume testing. The findings reveal that the MOCO algorithm surpasses the performance of the other algorithms, underscored by its capacity to uncover a diverse array of non-dominated solutions. To delve deeper into the experimental results, statistical analysis employing Friedman’s rank test is employed. The solutions generated and the convergence patterns exhibited by the MOCO approach underscore its exceptional proficiency in resolving intricate design problems.

Experimental study of the tension forming model of a long-span string-supported spoke-type truss structure

This paper investigates the structural response of the long-span string-supported spoke-type (LSSS) truss structure during the tension forming process, as well as the influences of the errors caused by initial defects of the structure. A 1:10 scaled test model was designed and fabricated with reference to the main hall structure of the Northwest University gymnasium. The mesh simplification and scaling-down of the design of the prototype were performed to obtain a test model with good similarity to the prototype. Subsequently, after the comparative analysis of different tensioning batches, numbers of tensioning stages, and tensioning sequences, a radial-cable-forming scheme of three-stage, five-batch, clockwise tensioning for each ring cables was determined to be superior for this type of system. The cable force, node vertical displacement, and rod stress were monitored during the test. SAP2000 finite element software was employed to establish a numerical model, which was then verified by the test results. The test results were found to be in good agreement with the simulation results. The outer-ring cables withstood a larger share of the load, which could provide more stiffness support for the structure. During the tensioning process, the tensioning of the inner-ring cables would further increase the vertical displacement of the outer-ring roof nodes, which increased the compressive stress of the upper-chord-rods near the outer-ring. After the tensioning was completed, the lower-chord-rods in the mid-span and at the ends of the truss were in tension. Comparative analyses of the variations of the position and geometry, as well as the cable force, in each ring of cables during the construction process demonstrated that initial defects in the installation of the upper roof will lead to the uneven distribution of the radial cable forces, and that the errors will gradually accumulate with the advancement of the tensioning stage. However, after the structure was formed, the verticality deviation of most struts was close to or less than 1/150, and the error between the measured value and the simulated value of the rod stress was basically kept below 10 %, which proved the rationality of the tension scheme adopted in the test.

Experimental investigations and finite element simulation for predicting wear life of overrunning clutches

An overrunning clutch, generally known as a freewheel clutch, is a direction dependent torque transmitting device that works on the principle of wedge friction. The overrunning wear characteristics of freewheels are studied using pin-on-disc tribometry. The wear experiments for freewheels are performed at accelerated loads to promote wear in a short period. The overrunning wear life of the clutch under operating conditions is predicted using an appropriate load-life relationship. A finite element-based Archard’s wear model is implemented as a numerical strategy to evaluate the wear profile. The maximum local wear for various loads is computed using experimentally obtained wear and friction coefficients. The numerical simulation is performed with an adaptive mesh technique utilizing incremental nodal displacements to predict surface wear. The experimental and numerical results are compared in terms of wear characteristics. The numerical wear results are almost 11% higher than the experimental results. The wear life of an overrunning clutch is predicted in terms of overrunning speed based on the wear amount.

Experimental study on the mechanical behavior of glulam suspendome considering the influence of prestressing

Integrating the prestressing system with the glulam reticulated shell, this study introduces an innovative glulam suspendome characterized by its exceptional span capability and great load-bearing capacity. Experimental research on the glulam suspendome was conducted considering various prestressing scenarios and loading conditions, incorporating both design load and quadruple design load assessments. Half-span loading was also introduced to explore the influence of asymmetric load. The results revealed that both the node displacements and the load exhibited linearity, implying that the structure remained in the elastic stage. Under full-span loading, the maximum strain was observed in the radial member with a value of −226με. Asymmetric load exerted a more adverse effect on the overall stability of glulam suspendome. With a prestress ratio of 1:2 between inner and outer cable, increasing outer cable force from 1.5 kN to 4.5 kN resulted in a 109.08 % reduction in displacement at the mid-span node under full-span loading, and a 98.04 % reduction during half-span loading. The increase in prestressing significantly improved the rigidity of glulam suspendome.

A variable-node element model and its application to damage analysis of RAC using the 2D base force element method

The existing methods find it difficult to resolve the inconsistency in the nodal displacements of nodes at the interface of dense and sparse element models. Therefore, this paper proposes a new variable-node element model using the base force element method (BFEM) and successfully applies it to study the mechanical properties of recycled aggregate concrete (RAC). First, the variable-node element model with an arbitrary change of node number in the mid-edges was established, and the explicit expressions of the 2 × 2 nodal compliance matrix and nodal displacements were given. Subsequently, the triangular and quadrilateral elements of single-sides and double-sides of hanging element models were developed based on the variable-node element model. In addition, a double-notched model of RAC with different aggregate types but the same aggregate distribution position was established, and numerical simulations of uniaxial tension were performed. The results show that the compliance matrix and nodal displacement are independent of the element characteristic without Gaussian integration. The variable-node hanging element model has high numerical accuracy and applicability, and the nodes between the sparse and dense meshes do not require any construction measures. The variable-node elements ensure the coordination of the nodal displacement at the interfaces. The aggregate shape has a significant effect on the damage mode, maximum principal strain, principal stress distribution, and stress concentration, while has a negligible effect on RAC tensile strength when the aggregate distribution is the same.

Research on the recovery performance of SMA tendon and the active control effect of adaptive cable dome

Cable dome is a widely used cable-strut tensile structure, and whose form is controllable. The shape and internal force of the structure can be adjusted by adjusting the length of the cable elements to enhance its load-bearing capacity. Shape memory alloy (SMA), as a new type of intelligent material, has excellent driving performance and is widely used in aerospace engineering, biotechnology, and construction engineering. In order to achieve active control of cable elements in cable domes using SMA, this paper conducted uniaxial tensile tests on SMA wires. Based on the test results, this paper designs and manufactures a SMA tendon suitable for active control and establishes a recovery performance model specifically for SMA tendon. Subsequently, tests on recovery performance are conducted to delve into the recovery force and displacement of the steel tendon. Finally, the SMA tendon is connected in series with the steel wire rope to obtain the active control cable elements, which is used to replace the diagonal cable in the Levy cable dome. Apply full span load to the structure, conduct active control tests by heating SMA tendon, record cable stress and node displacement during the test, and compare the results with finite element results and control methods in literature to study the control effect of SMA tendon. The test results show that the SMA tendon has good recovery performance and can be used as the control device of the control cable elements in the cable dome structure. The control effect is stable and reliable. Adjusting length of the diagonal cable can achieve Levy cable dome structural shape adjustment and improve the relaxation phenomenon of the ridge cable.

Development of optimization method for truss structure by quantum annealing

In this study, we developed a new method of topology optimization for truss structures by quantum annealing. To perform quantum annealing analysis with real variables, representation of real numbers as a sum of random number combinations is employed. The nodal displacement is expressed with binary variables. The Hamiltonian H is formulated on the basis of the elastic strain energy and position energy of a truss structure. It is confirmed that truss deformation analysis is possible by quantum annealing. For the analysis of the optimization method for the truss structure, the cross-sectional area of the truss is expressed with binary variables. The iterative calculation for the changes in displacement and cross-sectional area leads to the optimal structure under the prescribed boundary conditions.

Study on prestress distribution and structural performance of heptagonal six-five-strut alternated cable dome with inner hole

The cable dome structure is a highly efficient prestressed space structure with reasonable force, attractive shape, and large spanning capacity. It is increasingly widely used in stadiums, exhibition halls, terminals, and other large-scale public buildings and the roof structure of various transport hub projects. To solve the problem of weak overall structural stability of the traditional cable dome structure, a new type of prestressed space structure is proposed - heptagonal six-five-strut alternated cable dome with an inner hole. The composition of the structural system was given and a theoretical study of the distribution of structural prestress was carried out; based on the symmetry and periodicity conditions, the initial prestress distribution of the structure was accurately calculated using the node balance method, and the formulae for the geometric parameters of the structural cable-strut were derived; the numerical model was established by using the finite element software ANSYS 2022 R1, and the force characteristics of the structure under full-span uniform load, half span uniform live load, wind load, and temperature were studied. The effects of structural prestress, overall shape, and support stiffness, totaling three categories and six parameters, on the structural mechanical performance of the internal force of the member, node displacement, and support reaction force were analysed in detail and the sensitivity of the parameters is assessed quantitatively, accordingly, the values of the main design parameters such as thick-span ratio are given as suggestions. The analysis results show that the new structural system has a high load-carrying capacity and deformation resistance, and its proposal provides a new scheme and new ideas for the selection and design of the cable dome.

Form-finding of thermal-adaptive pin-bar assemblies based on eigenvalue modification

Lattice structures with tunable expansion properties have been investigated in multidisciplinary fields to control the temperature effects of structures or materials. The expected thermal adaptivity can be achieved by optimizing the structural geometry. A novel method for the form-finding of thermal-adaptive pin-bar assemblies is developed in this paper by considering the control of structural temperature effects as the minimization of the potential energy of the system. Based on the stationarity condition of the potential energy with respect to the nodal coordinates, the compatibility relationship between the thermal elongations of members and the target nodal displacements is proven to be the sufficient and necessary condition for structural thermal adaptivity. The solvability of the compatibility equation is determined by the rank equality between the compatibility matrix and its augmented form, which can be measured by the number of nonzero eigenvalues of its Gramian matrix. The analytical relationship between the eigenvalues of the Gramian matrix and the nodal coordinates is established using the matrix perturbation theory. A numerical strategy based on Newton’s method is proposed in which the eigenvalues are gradually modified by adjusting the nodal coordinates until the rank equality is satisfied. To address the existence of multiple solutions with structural thermal adaptivity, structural symmetry and periodicity constraints are introduced to narrow the solution space. The thermal-adaptive configurations of three illustrative pin-bar assemblies are analyzed using the proposed form-finding method, and the expected thermal deformations are verified for the obtained configurations using the finite element software ABAQUS. Comparing the results obtained by the proposed method with those obtained by nonlinear programming and the genetic algorithm validates the advantages of the proposed method in terms of computational time, optimality of the obtained configuration and applicability to complex structural geometries.

Spatial structure digital twins: Application in intelligent health monitoring of cable dome structures

Traditional structural health monitoring (SHM) based on contact sensors has drawbacks, such as high cost, susceptibility to interference, and narrow coverage. Digital twins (DTs) present an effective intelligent solution. However, the real-time monitoring of all structural components remains challenging due to high computational cost of high-order models in underlying framework. Additionally, the vast number of spatial structures globally and their long service time indicate the potential necessity of introducing SHM based on DT. In this context, this study proposed a reduced-order model-based DT framework for spatial structures. By compressing the experimental design samples, the multidimensional high-order physical models were reduced to several approximate low-order models for constructing a DT model, thereby achieving real-time calculation covering all components. The proposed framework was applied and validated through an experiment on a scale model of cable dome structure, and real-time interactive visualisation of monitoring data was displayed on a self-developed platform. The results demonstrate that the DT model enabled real-time presentation of calculation results (the calculation speed of <0.5 s/time), the mean relative error of cable tension monitoring was <3.85%, the strut stress monitoring could be controlled within 7.5%, and the mean absolute error of nodal displacement could be maintained at around 1 mm.

Study on the truss damage measurement based on Bayesian updating

Bayesian updating can integrate new observations in real time. This online updating property makes the Bayesian approach particularly suitable for dynamic monitoring of structural damage. In this paper, the node displacements are obtained by the finite element software OpenSees, assuming that the bars are damaged and the stiffness is reduced. Rejection Sampling method is used to determine the stiffness drop interval. During the sampling process, different load sizes, load locations, errors and types are selected to realize the updating of the stiffness of the top chord bar, bottom chord bar, vertical web bar, and diagonal web bar. A Pratt-type truss is used as an example, combined with displacement data. The proposed stiffness damage measurement method is demonstrated by updating the stiffness of four types of bars separately. The results shows that damage in structures can be accurately identified by Bayesian updating methods. This method not only pinpoints the location of the damage, but also quantifies the extent of the damage.

Surface accuracy prediction method for mesh reflector antenna considering uncertainty factors in manufacturing process

The cable-net structure of mesh reflector antenna meets the requirement of surface accuracy by optimizing the shape and tension. However, in the process of manufacturing and assembly, there are inevitable random errors and structure gravity, which lead to the displacement of the nodes in surface, the surface accuracy of the antenna decreases after fabrication eventually. It is challenging to analyze the uncertainty factors and the effects on the surface accuracy. Therefore, this paper analyzes the uncertainty factors of the antenna during fabrication and proposes a method to predict the surface accuracy of the antenna after manufacturing and assembly. Firstly, based on the equilibrium equation of the cable-net structure, the mechanism of node displacement induced by uncertainty factors leading to the reduction of surface accuracy is analyzed. Secondly, based on the structure characteristics and manufacturing conditions of the antenna, the uncertainty factors including cable-net manufacturing and assembly errors, cable-truss assembly errors and gravity are analyzed qualitatively and quantitatively, the distributions of the uncertainty factors are given. Thirdly, based on Monte Carlo method, the mean and interval of the surface accuracy of different dimension parameters are predicted, the empirical prediction formulas of the surface accuracy mean and interval are fitted. Finally, the accuracy and effectiveness of the proposed formulas are verified by several numerical simulations and surface accuracy measurement experiments. The prediction method can effectively guide the design and craft of large-aperture mesh reflector antenna.

Multi-material topology optimization with a direct meshless local Petrov–Galerkin method applied to a two-dimensional boundary value problem

ABSTRACT This work presents a novel approach for the solution of multi-material topology optimization problems of elastic structures coupling the Direct Meshless Local Petrov–Galerkin (DMLPG) method with the Gradual Bi-direction Evolutionary Structural Optimization (gBESO) method. In recent years, meshless methods have been used in several engineering fields, showing some advantages compared to mesh-based methods. DMLPG is a truly meshless method, which achieves results with good accuracy and computational efficiency, avoiding the numerical integration of complicated shape functions by adopting low-degree polynomials. In the proposed algorithm, DMLPG is used to obtain smooth nodal displacements, strains and stresses, and gBESO updates the structural geometry based on design sensitivity values of the compliance while it gradually increases the Young's modulus of the material. The optimization problem minimizes the compliance objective function subject to volume constraints. Numerical examples demonstrate the applicability and validity of the technique.

Comparative Study of G+6 Irregular Multistoryed Building of Different Shape of Diaphragm

Abstract: This study investigates the effectiveness of incorporating openings in the roof of re-entrant corner plan irregular buildings at different locations under earthquake loads. Five models with varying degrees of diaphragm discontinuity were analysed using STAAD Pro software. Node displacement, storey shear in X and Z directions, stress values, and maximum bending moment were evaluated to assess structural performance. Results indicate that models with higher diaphragm discontinuity exhibit increased node displacements, storey shear, and stress levels. Model M3, with 17% diaphragm discontinuity, consistently demonstrates superior performance in terms of lower displacements and stress values compared to other models. However, final model selection should consider specific project requirements and design considerations.

Comparative Study of G+6 Irregular Multistoryed Building of L Shape of Diaphragm Discontinuity

Abstract: This study investigates the effectiveness of incorporating roof openings in re-entrant corner plan irregular buildings at various locations under earthquake loads. Three models L-shaped diaphragm discontinuity were analyzed using STAAD Pro software. Node displacement and storey shear in both the X and Z directions were evaluated to assess structural performance. The results indicate that models with square diaphragm discontinuity exhibit increased node displacements and storey shear compared to those with L-shaped diaphragm discontinuity. The model with L-shaped diaphragm discontinuity consistently demonstrates superior performance in terms of lower displacements and shear stress values. However, the final model selection should take into account specific project requirements and design considerations.

Direct FE2 multiscale modeling of hydrogen-induced cracking in reactor pressure vessels

Leveraging on a recently developed multiscale simulation method, we propose a pioneering strategy for the multiscale analysis of hydrogen-induced cracking in reactor pressure vessels that considers micro-voids, their influences on hydrogen diffusion as well as the operating pressure of the vessel. In the finite element analysis, the nodal lattice hydrogen concentration and displacements are exchanged bi-directionally between the macroscale and microscale within a monolithic solution procedure. During the analysis, the voids are shown to cause non-uniform lattice hydrogen diffusion and the trapping effect, resulting in inter-void hydrogen accumulation, is demonstrated. Based on the hydrogen concentration on the void surfaces, the void hydrogen pressure was calculated for the hydrogen-induced cracking analysis. It was found that both internal shearing and necking failure modes exhibited micro-structure dependence. The internal shearing mode caused oriented through-wall propagation of cracks in the vessel pressure while the internal necking mode promoted void nucleation in the reactor pressure vessel. As a result, during the early stages of void evolution, the oriented internal shearing of the dispersed small voids showed a high possibility to induce through-wall failure of the reactor pressure vessel.

Static Stability Behavior-Based Seismic Damage Endurance Assessment of Long-Span Single-Layer Spherical Lattice Shells

ABSTRACT This paper presents a modified evaluation approach for the structural-capacity-reserve (SCR) based on the static stability behavior of single-layer spherical lattice shells to achieve more accurate assessment results of seismic damage endurance. The SCR index in this paper is calculated by integrating the redefined residual structural capacity (RSC) ratio based on post-earthquake static stability behavior within the range of damage degrees caused by strong earthquakes. Compared with the assessment work for seismic damage endurance in the existing literature, the proposed RSC ratio in this paper could take into account both ultimate load-bearing strength and residual deformation. Additionally, the specific quantitative indicator in the proposed assessment method should also be determined according to whether the residual nodal displacement of the lattice shell after an earthquake exceeds the limit value state specified by the design code. The numerical results in the case study indicate that the residual load-bearing strength of the lattice shell remains relatively constant under the same damage state induced by different earthquakes, with residual deformation significantly impacting the assessment of seismic damage endurance. Thereby, the required RSC can be controlled by reducing the residual nodal displacements of the lattice shell under strong earthquakes to achieve a well-balanced design scheme.

Permeability estimation for deformable porous media with convolutional neural network

PurposeAccurately evaluating fluid flow behaviors and determining permeability for deforming porous media is time-consuming and remains challenging. This paper aims to propose a novel machine-learning method for the rapid estimation of permeability of porous media at different deformation stages constrained by hydro-mechanical coupling analysis.Design/methodology/approachA convolutional neural network (CNN) is proposed in this paper, which is guided by the results of finite element coupling analysis of equilibrium equation for mechanical deformation and Boltzmann equation for fluid dynamics during the hydro-mechanical coupling process [denoted as Finite element lattice Boltzmann model (FELBM) in this paper]. The FELBM ensures the Lattice Boltzmann analysis of coupled fluid flow with an unstructured mesh, which varies with the corresponding nodal displacement resulting from mechanical deformation. It provides reliable label data for permeability estimation at different stages using CNN.FindingsThe proposed CNN can rapidly and accurately estimate the permeability of deformable porous media, significantly reducing processing time. The application studies demonstrate high accuracy in predicting the permeability of deformable porous media for both the test and validation sets. The corresponding correlation coefficients (R2) is 0.93 for the validation set, and the R2 for the test set A and test set B are 0.93 and 0.94, respectively.Originality/valueThis study proposes an innovative approach with the CNN to rapidly estimate permeability in porous media under dynamic deformations, guided by FELBM coupling analysis. The fast and accurate performance of CNN underscores its promising potential for future applications.

Efficient Sizing and Layout Optimization of Truss Benchmark Structures Using ISRES Algorithm

This paper presents a comprehensive investigation into the application of the Improved Stochastic Ranking Evolution Strategy (ISRES) algorithm for the sizing and layout optimization of truss benchmark structures. Truss structures play a crucial role in engineering and architecture, and optimizing their designs can lead to more efficient and cost-effective solutions. The ISRES algorithm, known for its effectiveness in multi-objective optimization, is adapted for the single-objective optimization of truss designs with multiple design constraints. This study encompasses a wide range of truss benchmark structures, including 10-bar, 15-bar, 18-bar, 25-bar, and 72-bar configurations, each subjected to distinct loading conditions and stress constraints. The objective is to minimize the truss weight while ensuring stress and displacement limits are met. Through extensive experimentation, the ISRES algorithm demonstrates its ability to efficiently explore the solution space and converge to optimal solutions for each truss benchmark structure. The algorithm effectively handles the complexity of the problems, which involve numerous design variables, stress constraints, and nodal displacement limits. A comparative analysis is conducted to assess the performance of the ISRES algorithm against other state-of-the-art optimization methods reported in the literature. The comparison evaluates the quality of the solutions and the computational efficiency of each method. Furthermore, the optimized truss designs are subjected to finite element analysis to validate their structural integrity and stability. The verification process confirms that the designs adhere to the imposed constraints, ensuring the safety and reliability of the final truss configurations. The results of this study demonstrate the efficacy of the ISRES algorithm in providing practical and reliable solutions for the sizing and layout optimization of truss benchmark structures. The algorithm’s competitive performance and robustness make it a valuable tool for structural engineers and designers, offering a versatile and powerful approach for complex engineering optimization tasks. Overall, the findings contribute to the advancement of optimization techniques in structural engineering, promoting the development of more efficient and cost-effective truss designs for a wide range of engineering and architectural applications. The study’s insights empower practitioners to make informed decisions in selecting appropriate optimization strategies for complex truss-design scenarios, fostering advancements in structural engineering and sustainable design practices.

Extension of the a posteriori finite element method (APFEM) to geometrical alterations and application to stochastic homogenisation

AbstractWe recently proposed an efficient method facilitating the parametric study of a finite element mechanical simulation as a postprocessing step, that is, without the need to run multiple simulations: the a posteriori finite element method (APFEM). APFEM only requires the knowledge of the vertices of the parameter space and is able to predict accurately how the degrees of freedom of a simulation, i.e., nodal displacements, and other outputs of interests, for example, element stress tensors, evolve when simulation parameters vary within their predefined ranges. In our previous work, these parameters were restricted to material properties and loading conditions. Here, we extend the APFEM to additionally account for changes in the original geometry. This is achieved by defining an intermediary reference frame whose mapping is defined stochastically in the weak form. Subsequent deformation is then reached by correcting for this stochastic variation in the reference frame through multiplicative decomposition of the deformation gradient tensor. The resulting framework is shown here to provide accurate mechanical predictions for relevant applications of increasing complexity: (i) quantifying the stress concentration factor of a plate under uniaxial loading with one and two elliptical holes of varying eccentricities, and (ii) performing the stochastic homogenisation of a composite plate with uncertain mechanical properties and geometry inclusion. This extension of APFEM completes our original approach to account parametrically for geometrical alterations, in addition to boundary conditions and material properties. The advantages of this approach in our original work in terms of stochastic prediction, uncertainty quantification, structural and material optimisation and Bayesian inferences are all naturally conserved.