Nonlinear Finite Element Method Research Articles

Method for Parameter Tuning of Hybrid Optimization Algorithms for Problems with High Computational Costs of Objective Function Evaluations

In this paper, the authors focus on presenting the methodology for tuning optimization algorithm parameters, with a special focus on evolutionary algorithm applications. The problem considered concerns the phenomenon of nonlinear buckling of the automotive shock absorber, which itself is solved using a commercial application of the finite element method (FEM) simulation. These analyses are usually time-consuming; therefore, the authors decided to use a surrogate model, which mimics the behavior of the actual nonlinear FEM simulation. Surrogate modeling (metamodeling) is utilized to drastically shorten the simulation time, and thus study numerous algorithm parameter combinations, allowing for tuning them and providing a robust and efficient tool for optimization. The example shown in this paper is related to the minimization of the shock absorber weight, taking into account the stability of the system. The presented method can be used in any optimization problem where the high computational cost of objective function evaluations prevents tuning of the algorithm parameters.

Research on the control limits of cable length errors of cable-strut tensile structures for prestressed relaxation under load effect

Cable-strut tensile structures (CSTS) are mainly composed of cables, and the cable length errors are bound to exist in the manufacturing of cables. The cable length errors have significant impacts on the mechanical properties of CSTS under load effects. Meanwhile, CSTS generally uses flexible membrane material as roofs, therefore cable length errors will result in the wrinkle of roofs and then cause the secondary accumulation effects of rain and snow load. Therefore, it is necessary to reasonably control the manufacturing errors of cable length. In order to solve the problem, the method of solving the control limits of cable length errors of CSTS is proposed due to the prestressed relaxation under load effects. The reliability index of CSTS is firstly given based on the reliability theory. Then, based on the reliability index and the criterion of prestress relaxation under load effect, the critical state equation and constraint inequality group are constructed, and the coefficient matrix of constraint inequality group is derived. Meanwhile, the nonlinear finite element method for solving the coefficient matrix of constraint inequality group is proposed. The procedure of solving the control limits of cable length errors of CSTS is given based on the proposed method. The crossed spoke cable-truss structure is taken as an example to verify the feasibility of the new method. The research contents provide an effective solution for controlling cable length errors of CSTS for prestressed relaxation under load effect.

Seismic damage prediction of RC buildings using machine learning

AbstractDecision‐makers and stakeholders require a rapid assessment of potential damage after earthquake events in order to develop and implement disaster risk reduction strategies and to respond systematically in post‐disaster situations. The damage investigated manually after an earthquake are complicated, labor‐intensive, time‐consuming, and error prone process. The development of fragility curves is time consuming and unable to predict the damage for wide classes of structures since it considers few structural properties and only one seismic characteristic. Furthermore, the nonlinear finite element method cannot be utilized for numerous buildings because it involves more time and money. This paper presents the machine learning (ML)‐based seismic damage prediction of RC buildings. It is found that some of the research works only considered seismic parameters or structural parameters to train the ML models and predict the structural damage assessment. However, these ML models may not fully reveal the underlying complexity of the relationship between input parameters and building performance. As a result, their applicability will be limited. This paper evaluates the feasibility of using ML techniques such as K‐nearest neighbor, random forest, decision tree, support vector machine, and artificial neural network to rapidly predict earthquake‐induced reinforced concrete building damage considering both the structural properties and ground motion characteristics. The machine learning models are trained using the simulation results. Due to lack of real earthquake damage datasets or limited access, most of the research works used Scikit Learn train_test_split function to randomly split the entire datasets into training and testing datasets and the performance of the proposed ML technique are evaluated using the testing datasets. However, in this study, the performances of different ML models are evaluated using real earthquake damage datasets of RC buildings collected after 2015 Nepal earthquake. The overall accuracy on testing datasets suggests the capability of machine learning algorithms in successfully predicting the seismic damage of reinforced concrete buildings in quick time with reasonable accuracy. This study is beneficial in emergency response and recovery planning after an earthquake.

A nonlinear stochastic finite element method for solving elastoplastic problems with uncertainties

AbstractThis article presents an efficient nonlinear stochastic finite element method to solve stochastic elastoplastic problems. Similar to deterministic elastoplastic problems, we describe history‐dependent stochastic elastoplastic behavior utilizing a series of (pseudo) time steps and go further to solve the corresponding stochastic solutions. For each time step, the original stochastic elastoplastic problem is considered as a time‐independent nonlinear stochastic problem with initial values given by stochastic displacements, stochastic strains, and internal variables of the previous time step. To solve the stochastic solution at each time step, the corresponding nonlinear stochastic problem is transformed into a set of linearized stochastic finite element equations by means of finite element discretization and a stochastic Newton linearization, while the stochastic solution at each time step is approximated by a sum of the products of random variables and deterministic vectors. Each couple of the random variable and the deterministic vector is also used to approximate the stochastic solution of the corresponding linearized stochastic finite element equation that can be solved via a weakly intrusive method. In this method, the deterministic vector is computed by solving deterministic linear finite element equations, and corresponding random variables are solved by a non‐intrusive method. Further, the proposed method avoids the curse of dimensionality successfully since its computational effort does not increase dramatically as the stochastic dimensionality increases. Four numerical cases are used to demonstrate the good performance of the proposed method.

A nonlinear finite element method for analyzing the bending behavior of functionally graded shape memory alloys under the loading process

A nonlinear finite element method for analyzing the bending behavior of functionally graded shape memory alloys under the loading process

Slamming loads and responses on a non-prismatic stiffened aluminium wedge: Part II. Numerical simulations

An experimental study was carried out to examine the impact-induced loads and structural responses of a three-dimensional non-prismatic aluminium wedge. The findings of the experimental study were presented in the first part of this publication, entitled “Slamming loads and responses on a non-prismatic stiffened aluminium wedge: Part I. Experimental study.” This paper describes the second part of the study, which deals with numerical simulations of slamming loads acting on the wedge and its dynamic responses. Two different two-way coupling methods are assessed and compared to simulate the water entry problem. Initially, an explicit nonlinear finite element method with a Multi-Material Arbitrary Lagrangian-Eulerian (MMALE) solver is employed to evaluate the elastic response of the structure following a free-fall water impact. Subsequently, the hydroelastic slamming problem is modelled using a two-way coupled technique with a k-ε turbulence model and implicit unsteady solver for both the fluid and structural domains (Star-CCM+/ABAQUS). The effect of viscosity on slamming loads and responses was examined, and numerical results are compared with experimental data. To investigate the effect of rigidity on structural response and bottom deflection, the wedge was designed with bottom plates of varying thickness. The computed results from the two numerical models and the experimental data are in good agreement. The study concluded that the bottom plates deformation affects hydrodynamic loads during slamming. It is also observed that impact-induced loads depend on the water impact velocity and the flexibility of the bottom plates. This suggests that the slamming pressure increases with an increase in impact velocity and decreases when the structures become more flexible. According to this study, both numerical models are suitable for accurate and efficient computations of hydroelastic slamming; however, the MMALE method results in larger numerical fluctuations.

Ultimate Shear Strength of Pitted Plates with Crack Using Finite Element Method

_ Ultimate strength of thin steel plates was studied under shear loading when pitting corrosion and cracking occur simultaneously. Nonlinear finite element method was used and the effects of different geometrical parameters, such as crack position, crack length, pit depth, pit diameter, number of the pits, and the inclination angle of the crack, were investigated. It was found that the degree of the pitting (DOP) significantly reduces the ultimate shear strength of the pitted plates when the corrosion is low. For high amount of corrosion, the reduction of the ultimate shear strength remains the same regardless of the amount of the DOP. In plates with short cracks, the crack length has no influence on the reduction of the ultimate shear strength. Also, it was found that the position of the crack is more effective than the length of the crack on the reduction of the ultimate shear strength of the cracked plates. In the cracked-pitted plates, there was no interaction between crack and pit for extremes value of DOP. For low value of DOP, the ultimate shear strength of the cracked-pitted plate was the same as the cracked plate, and for large value of DOP, it is the same as pitted plate. Introduction According to a study performed between 2002 and 2008 by American Bureau of Shipping (ABS) (“Review of Current Practices of Fracture” 2012), majority of reported fractures of the ships were structural failures, such as weld defect, buckling, fracture, and cracking. Cracks and corrosion are two more common defects, which are the main reasons of the failure of the aged steel structures. Plates and stiffened plates are the main structural elements in many structures, including airplanes, bridges, offshore structures, and ships. Ultimate strength evaluation of these structural elements is crucial for rational design of structures, such as Load Resistance Factor Design (LRFD) methods in civil engineering and Ultimate Strength (UTS) evaluation in ship structure. Many studies are carried out to evaluate ultimate strength of intact and damaged plates/ stiffened plates under in-plane compressive stress. Ranji (2012) studied ultimate strength of plate with general corrosion under in-plane compression. He proposed a spectrum for random generation of corroded surface and ultimate strength of corroded plate was evaluated using computer code ANSYS. Ranji and Zarookian (2015) analyzed ultimate strength of cracked stiffened plates with cracks having different stiffeners numerically.

External airway splint placement for severe pediatric tracheobronchomalacia

ObjectiveTo present external airway splinting with bioabsorbable airway supportive devices (ASD) for severe, life-threatening cases of pediatric tracheomalacia (TM) or tracheobronchomalacia (TBM). MethodsA retrospective cohort was performed for 5 pediatric patients with severe TM or TBM who underwent ASD placement. Devices were designed and 3D-printed from a bioabsorbable material, polycaprolactone (PCL). Pre-operative planning included 3-dimensional airway modeling of tracheal collapse and tracheal suture placement using nonlinear finite element (FE) methods. Pre-operative modeling revealed that triads along the ASD open edges and center were the most effective suture locations for optimizing airway patency. Pediatric cardiothoracic surgery and otolaryngology applied the ASDs by suspending the trachea to the ASD with synchronous bronchoscopy. Respiratory needs were trended for all cases. Data from pediatric patients with tracheostomy and diagnosis of TM or TBM, but without ASD, were included for discussion. ResultsFive patients (2 Females, 3 Males, ages 2–9 months at time of ASD) were included. Three patients were unable to wean from respiratory support after vascular ring division; all three weaned to room air post-ASD. Two patients received tracheostomies prior to ASD placement, but continued to experience apparent life-threatening events (ALTE) and required ventilation with supraphysiologic ventilator settings. One patient weaned respiratory support successfully after ASD placement. The last patient died post-ASD due to significant respiratory co-morbidity. ConclusionASD can significantly benefit patients with severe, unrelenting tracheomalacia or tracheobronchomalacia. Proper multidisciplinary case deliberation and selection are key to success with ASD. Pre-operative airway modeling allows proper suture placement to optimally address the underlying airway collapse.

Accelerated nonlinear finite element method for analysis of isotropic hyperelastic materials nonlinear deformations

In this work, an approximate Jacobian matrix is proposed based on the total Lagrangian formulation of Finite Element Method for isotropic hyperelastic materials. The approximate Jacobian matrix can take the place of the exact Jacobian matrix in the Newton–Raphson method to avoid frequent construction and factorization of the Jacobian matrix. A new Quasi–Newton method employing the approximate Jacobian matrix is developed to significantly improve the convergence rate. The proposed method was tested on three examples with the combinations of three hyperelastic material models and three element types. The results show that the proposed method is more efficient than ABAQUS and CALCULIX (an open-source FEM software package) on all of the tests without loss of accuracy. It is up to 100 times faster than the traditional Quasi–Newton method, and at least 2.5 times faster than ABAQUS.

Assessment of the stiffened panel performance in the OTEC seawater tank design: Parametric study and sensitivity analysis

Ocean thermal energy conversion (OTEC) is a process of generating electricity by exploiting the temperature difference between warm surface seawater and cold deep seawater. Due to the high static and dynamic pressures that are caused by seawater circulation, the stiffened panel that constitutes a seawater tank may undergo a reduction in ultimate strength. The current paper investigates the design of stiffening systems for OTEC seawater tanks by examining the effects of stiffening parameters such as stiffener sizes and span-over-bay ratio for the applied combined loadings of lateral and transverse pressure by fluid motion and axial compression due to global bending moment. The ultimate strength calculation was conducted by using the non-linear finite element method via the commercial software known as ABAQUS. The stress and deformation distribution due to pressure loads was computed in the first step and then brought to the second step, in which the axial compression was applied. The effects of pressure on the ultimate strength of the stiffener were investigated for representative stiffened panels, and the significance of the stiffener parameters was assessed by using the sensitivity analysis method. As a result, the ultimate strength was reduced by approximately 1.5% for the span-over-bay ratio of 3 and by 7% for the span-over-bay ratio of 6.

Large-amplitude vibration of rotating functionally graded blades including geometrical nonlinearity and stress stiffening effects

The nonlinear frequency responses of functionally graded (ceramic/metal/ceramic) straight/curved blade-type structures are examined under rotation and thermal environment. Here, the geometrical nonlinearity is introduced using Green-Lagrange’s strain via the higher-order shear deformation theory. The constituent materials, i.e. ceramic and metal-alloy, are considered to be temperature-dependent, whereas, the overall blade material properties are evaluated using Voigt’s homogenization scheme via a modified power-law function. The equations of motion are obtained using Hamilton’s principle by including the geometrical nonlinearity and stress stiffening effects. The linear and the nonlinear frequency responses are computed through the developed nonlinear finite element method and Picard’s successive iteration scheme. An exhaustive computation is carried out to report the linear and the nonlinear vibrational behavior of the proposed composite straight/curved blade model at small-to-large amplitudes for various sets of combinations of geometric and material parameters, such as blade span, blade thickness, volume fractions, rotational speed, and temperature.

Research on the Vibration Response of an Aircraft Gun Muzzle Based on Nonlinear Finite Element

The muzzle vibration response of an aircraft gun is one of the key factors affecting the firing accuracy of the aircraft gun. In order to study the muzzle vibration response of an aircraft gun, based on the basic theory of the nonlinear finite element method, the nonlinear finite element dynamics simulation model is established by considering the nonlinear factors which are the contact and collision between the gun aircraft and the cradle, the contact and collision between the elevating gear arc and gear, and the slide clearance between the aircraft gun and the cradle, etc. The muzzle vibration response is characterized by the linear displacement and linear velocity of the center point of the aircraft gun, and its dynamics is obtained through numerical calculation and simulation. The correctness of the dynamics simulation model of the aircraft gun muzzle vibration is verified by setting up verfication bench. The results show that the established nonlinear finite element dynamic simulation model can be used to predict the muzzle vibration response of the aircraft gun, and at the same time, by changing the slide clearance between the aircraft gun and the cradle, the effect of clearance on the muzzle vibration response is investigated. Additionally, it can be seen that reducing the slide clearance can improve the firing accuracy of the aircraft gun while ensuring the machining assembly and mechanism movement.

Multiscale analysis of nano-powder compaction process using the FEM–MD technique

In this paper, a continuum–atomistic (FEM–MD) multiscale technique is developed for modeling the compaction process of metallic nano-powders. Nano-powders are assumed as the continuum body that are modeled using the nonlinear finite element method (FEM). Representative volume element (RVE) consists of a number of nanoparticles to reflect the discrete nature of nano-powders. The atomistic RVEs are modeled using the molecular dynamics (MD) method to capture the plastic deformation of nanoparticles under the compaction process. The MD analysis of atomistic RVEs provides the feasibility of modeling the friction and interaction of nanoparticles. A parametric study is performed over the atomistic RVEs to evaluate the influence of various parameters, such as the type of boundary conditions, width of boundary layer, size and number of nanoparticles, and compaction velocity on the densification behavior of nano-powders. The effect of die-wall friction is investigated on the compaction behavior of nano-powders by evolution of die-wall friction coefficient for different values of compaction velocity and temperature. The accuracy of multiscale analysis is verified by comparing the numerical results with those of experimental data for the uniaxial compaction test. The performance of proposed computational method is finally presented in modeling the micro-cylindrical bush and micro-tablet components during the compaction process of micro-scale metallic nano-powders.

Numerical approach for flexible body with internal boundary movement

In this paper, a numerical method is proposed for a flexible tether motion that spans two different environments and has large displacement and deformation. When considering the behavior of a tethered system in which the tether cable is subjected to the above conditions, variations of an internal boundary in the tether must be considered. In general, the absolute nodal coordinate formulation (ANCF), a nonlinear finite element method, is effective for the dynamic simulation of a flexible body with large displacement and deformation. However, in conventional methods, such as ANCF, the analysis accuracy decreases and the calculation cost increases when the movement of an internal boundary across different environments is considered. In this study, an efficient numerical approach that considers the variations of an internal boundary by using ANCF using variable-domain finite elements is proposed. In addition, to further improve the calculation efficiency, dimensionless variables are introduced using appropriate representative values. The accuracy of the numerical results obtained using the proposed method, which considers an internal variable boundary, is similar to that for a conventional method.

Fluid-structure interaction simulation for performance prediction and design optimization of parafoils

Parachute design is challenging to achieve innovative progress if the dominant role of testing continues, as it will be an increasingly expensive and time-consuming work. The aim of this study is to establish a reliable and efficient design tool using existing advanced numerical modeling methods. This paper presents a numerical method based on two-way coupled fluid-structure interaction (FSI) strategies for predicting aerodynamic and flight performance for parafoil design optimization. The nonlinear finite element method was used for the canopy fabric model and flow field, and the fluid dynamics were solved by Reynolds-averaged Navier-Stokes with the Spalart-Allmaras turbulence model. The FSI simulations are performed to assess the aerodynamic performance and structural deformations of full-scale parafoil canopies. The equilibrium shape of the parafoil canopy under steady gliding states and the relevant flow field were analyzed to enhance confidence and understanding in the performance prediction of new parachutes. Three-dimensional FSI simulation results of parafoils show that the inflation caused flexible bulges of canopy cells, and the maximum lift coefficient increased more than 16% with a higher stall angle of attack than that of the rigid body model. A parafoil with a smaller leading edge inlet or a scaling down area can improve the aerodynamic performance, mainly manifested in a higher lift-to-drag ratio and better anti-stall performance. Finally, the prediction results of parafoil glide performance were verified by flight test data, and the prediction accuracy of the flexible model is more than 10% higher than that of the rigid model. This work makes the simulation tools a step closer to practical application.

Investigation for stress–strain curves of the plastic damage model for concrete

The Barcelona model is one of the most widespread models used in the nonlinear finite element method for simulating the real behavior of concrete. The strong robustness of this model can be attributed to two main reasons, the first one being its ability to account for the elastic stiffness degradation induced by plastic straining and the second one the aptness of considering the stiffness recovery effects under cyclic loading. This model was examined in the paper by comparing the generated stress–strain diagrams with several analytical solutions from the literature. The comparing process in the compression and tension cases with the closed-form solutions of Desayi, Krätzig, Lubliner and Thorenfeldt proved that the Barcelona model provided identical outcomes with Lubliner’s formula, which was used as the hardening function in the finite element implementation of this model. What is more, this model provided the same curves in case of the others in the ascending branches, and for the descending branch, this study proved that the outcomes of the Barcelona model are completely different from the ones of Desayi in the compression case and slightly similar to Thorenfeldt’s curves in the tension case.

Bio-inspired design, modeling, and 3D printing of lattice-based scale model scooter decks

This research aims at enhancing the performance of scale-model scooter decks by investigating various architected cellular metamaterial and bio-inspired core structure designs, such as honeycomb, tetrachiral, re-entrant, arrowhead, and star-shaped arrangements. An initial effort is made toward the design and rapid prototyping of small-scale deck with a uniform honeycomb core structure. More specifically, polylactic acid is utilized to fabricate complex structures via fused filament fabrication technique. Investigation is then focused on its mechanical performance, such as its bending properties obtained through a three-point bending test. Simulations are also conducted with different core configurations using a geometrically non-linear finite element method which is implemented. Experiments are carried out to verify the numerical results. After validation, various patterns are modeled, and eventually, it is observed that the functionally graded arrowhead structure has the best bending resistance, compared to other bio-inspired and mechanical metamaterial structures. At a constant force of 845 N, the functionally graded arrowhead design lowers the deflection in the middle of the scale model of scooter deck by up to 14.7%, compared to the uniform arrowhead structure. Furthermore, comparing the tetrachiral and functionally graded arrowhead configurations at a constant force, a 30% reduction in central deflection was observed. Due to the lack of similar results and designs in the specialized literature, this work could potentially advance the state-of-the-art scooter core designs and provide designers with architectures that could enhance the performance and safety of scooters.

Design and analysis of a triangular bi-axial flexure hinge

To achieve the requirement of flexure hinges for specific optical precision equipment, a new triangular bi-axial flexure hinge is proposed. The analysis model for the flexibility of the triangular bi-axial flexure hinges is derived. After that, the linear and nonlinear finite element methods are used to verify the analysis model. Then, the physical dimensions of the hinge are optimized using the multi-island genetic algorithm in conjunction with the finite element method, and the rotational stiffness and center drift are diminished. Static analysis and modal analysis of the hinge are conducted. A test system was built to gage the flexure hinge’s rotational stiffness. The results demonstrated that there was good agreement between the analytically calculated value, simulated calculated value, and experimental value. To summarize, the analysis model met the design requirements of the triangular bi-axial flexible hinge, and the multi-island genetic algorithm effectively optimized the physical dimensions of the hinge and enhanced its performance. The design process provides new ideas for the design of other forms of hinges.

Geomechanical assessment of a large-scale CO2 storage and insights from uncertainty analysis

Geological storage of CO2 provides a feasible solution to curb CO2 emissions to the atmosphere and relieve climate change. However, as CO2 is injected into the reservoir, the increased pore pressure may result in fault reactivations or damaging geomechanical changes to the caprock, which could be detrimental to the containment of injected CO2. On the other hand, uncertainty is inevitable due to the limited information of the complex subsurface system. In this study, we develop a workflow to assess the geomechanical impact of CO2 geological storage and include management of sources of uncertainties associated with the subsurface system. We utilize the hypothetical large-scale carbon sequestration situated in the Southern San Joaquin Valley in California, USA as a case study. We firstly set up a three-dimensional (3D) geomechanical model using a non-linear quasi-static finite element method. The applied workflow has features including: (1) Coulomb friction behavior to model fault slippage, (2) CAD representation of land surface and faults, (3) non-uniform pressure increase based on dynamic reservoir simulations, and (4) variable rock properties for formation layers. We perform uncertainty analyses using a response surface methodology and a Box-Behnken design to assess the significance of subsurface uncertainties to geomechanical responses. We find that the intact caprock will not have a shear failure even considering the subsurface uncertainties. However, the faults can reactivate and give potential flow pathways in the caprock. The presented workflow integrates advanced geomechanical models and uncertainty analysis, which can be readily applied to other CO2 storage projects to mitigate geomechanical sources of risk.

Influence of the design constraints on the thickness optimization of glass panes to achieve lightweight insulating glass units in cruise ships

The increasing complexity and size in cruise ships demands for lightweight structures and practical but accurate design methods. Conventionally, the focus has been on the steel parts of the ship, as they make most of its weight. However, the proportions of other materials are increasing. Therefore, this study attempts to provide better understanding how one could reach the lightweight designs of insulating glass units (IGUs) in ships. These are windows where at least two glass panes are separated by a hermetically sealed cavity. They are thin-walled structures that benefit not only from the geometrically nonlinear behavior, but also from the load sharing. Considering these effects, their behavior is studied using the nonlinear Finite Element Method and Particle Swarm Optimization. Different design criteria are imposed on the thickness determination of the glass panes with different shapes. Rectangular, triangular, and circular shapes are considered. The results show that the triangular shapes have the least weight for a given area when the deflection criterion is the dominating one. When maximum principal stress is the thickness defining criterion, the shapes perform almost equally well. The ratio between the pane thicknesses had the most influence on the behavior of the IGU. As it increases, i.e., one pane is significantly thicker than the other, the load sharing percentage drops, but it provides the most lightweight solution. Closer it is to 1, more equally the structural stresses are divided between the panes, i.e., redundancy is achieved. Finally, it is possible to establish a simple but effective method for the thickness determination of these IGUs using the results of this study. However, more work is required, including numerical analysis and experimental testing.