One-dimensional Beam Element Research Articles

Moving Finite Element Mesh Modelling for Induced Vibration Estimation of Moving Vehicles on Infinite Elastic Media

This paper describes the development of one-dimensional beam elements and 3D finite elements with moving meshes for applications on induced vibration due to moving loads (or moving vehicles in contact with the rail or road) in a semi-infinite elastic homogeneous media, such as trains on railroad track or vehicles on roads. A conventional finite-element strategy requires very large meshes to allow the estimation of induced vibration of a moving vehicle, because a large portion of the mesh is required to model the distance travelled by the vehicle during simulation, in addition to a domain required at both sides of the model to separate the boundaries so that no undesired boundary effects are presented. An alternative approach is the use of moving elements to ensure that the loads do not approach the boundaries of the model, determining a significant reduction of the mesh. The moving mesh moves at the speed of the vehicle, maintaining the contact points location in the moving reference frame. This determines that a time-invariant model can be obtained for constant velocity analysis in the case of homogeneous media. One important aspect of the formulation is the asymmetric nature of stiffness and damping matrices of the finite element model due to the effects of velocity of the moving mesh. Random process modelling of roughness of the rails or road allows the assessment of its effect on induced vibration of moving vehicles on infinite media. Different vehicle models can be connected the moving mesh model, including different number of wheel axes by defining nodes of the mesh bellow each wheel, making the formulation very practical. Some application examples of the modelling technique are presented and limitations of the technique are mentioned.

Optimized analysis and reinforcement design model for RC/SCC box-section bridges using developed advanced design framework

In recent years, there has been a significant rise in the construction of reinforced concrete (RC) and steel-concrete composite (SCC) box-section bridges. However, design codes do not provide specific design methods for the RC plates of such bridges where the plates experience both intricate forces and moments. The current design approaches are primarily based on conventional one-dimensional beam element theory, which neglects the complex spatial force characteristics of the structural elements, potentially leading to unsafe design. Therefore, it is imperative to address this issue. To bridge this gap, a comprehensive analysis and reinforcement design procedure named as the developed advanced design framework (DADF) is proposed in this study. The spatial analysis of bridges was performed using a refined numerical model, called the spatial grid model (SGM), to consider the structural spatial effects with limited model scales. Subsequently, the internal force corresponding matrix (IFCM) was implemented through Python scripts to determine the most critical internal force combination for an RC plate element. Additionally, the three-layered sandwich model (T-LSM) was employed with limit analysis to automatically design reinforcement for all elements, serving as a practical tool for design. This research demonstrates that the implementation of the DADF can significantly reduce steel reinforcement in the RC plates of such bridges by up to 48 %, and 23 % in total, showcasing the efficiency of the developed framework. Overall, the findings emphasize that the proposed DADF offers a robust procedure for steel reinforcement design of RC/SCC box-section bridges.

Multi-segmented fifth-order polynomial–shaped shells under hydrostatic pressure

The design and construction of submerged complex shells for new applications in offshore structures are increasingly popular. Therefore, the purpose of this study is to present the analytical model and Lagrange multipliers associated with the constraint equation for large displacement analysis of a fifth-order polynomial–shaped shell under hydrostatic pressure for the first time. The shell geometry can be computed using differential geometry with a fifth-order polynomial. The energy functional of the fifth-order polynomial–shaped shell is derived based on the principle of virtual work and written in the appropriate form. The nonlinear static responses of the fifth-order polynomial–shaped shell under hydrostatic pressure can be calculated using the nonlinear finite element method via the fifth-order polynomial shape function. This study develops the model using one-dimensional beam elements divided along the shell radius. To avoid the slope of a meridian curve at the equatorial plane approaching infinity, the shell is divided into two regions defined by different surface parameters. At the junction of two adjacent regions, the continuity requirements are established as the constraint conditions using Lagrange multipliers. The numerical results from the proposed methods are demonstrated and discussed, along with the effects of varied seawater depth, thickness, and elastic modulus on the deformed configuration and principal curvature at the deformed state. The results show that the nonlinear displacement is higher than the linear one in the case of the hydrostatic pressure, whereas the case of the internal pressure has an opposite result. For principal curvatures at the apex, the principal curvatures increase as the seawater depth increases, whereas the principal curvatures decrease when the thickness and elastic modulus increase.

Mesoscopic evaluation of the bond behavior of concrete with deformed rebar subjected to passive confinement employing 3D discrete model

The bond between concrete and steel is one of the most critical properties of reinforced concrete and affects the overall structural performance. The current research realistically evaluates the macroscopic bond behavior, quantitatively highlights the detailed internal fracture process, and clarifies the internal fracture mechanism. The numerical analyses are conducted for cover confinement effects employing the coupled Rigid Body Spring Model (RBSM) and the nonlinear solid Finite Element Method (FEM) model with varying cover thicknesses and rebar diameters. The modeling of concrete and deformed rebar considering the actual geometrical features is performed employing 3D-RBSM and solid FEM, respectively. It has been determined that the mesoscopic numerical model adequately simulates the test stress-slip relationships, demonstrates the increasing tendency of peak stress and peak slip against the increase in cover thickness, and reproduces the post-peak softening. The model enables simulation of splitting failure with a small cover thickness and the transformation of failure into pull-out and showed the enhancement of peak stress and ductility with a large cover, while reproducing the splitting as well as pull-out for medium cover. Furthermore, the model accurately reproduces the different bond and internal crack propagation caused by variations in bearing stress and radial pressure against different rebar diameters. The model precisely captured the radial fractures arising from the ribs, such as Goto cracks, which is not possible using conventional one-dimensional beam elements to represent the reinforcing bar.

Modal analysis of rigid pavement resting on two-parameter soil foundation model using finite element framework

PurposeThe purpose of this study is to numerically model the rigid pavement resting on two-parameter soil and to examine its modal parameters.Design/methodology/approachThis study is carried out using a one-dimensional beam element with three rotational and three translational degrees of freedom based on the finite element method. MATLAB programming is used to perform the free vibration analysis of the rigid pavement.FindingsCyclic frequency and their corresponding mode shapes were determined. It has been investigated how cyclic frequency changes as a result of variations in the thickness, span length of pavement, shear modulus, modulus of subgrade, different boundary conditions and element discretization. Thickness of the pavement and span length has greater effect on the cyclic frequency. Maximum increase of 29.7% is found on increasing the thickness, whereas the cyclic frequency decreases by 63.49% on increasing span length of pavement.Research limitations/implicationsThe pavement's free vibration is the sole subject of the current investigation. This study limits for the preliminary design phase of rigid pavements, where a complete three-dimensional finite element analysis is unnecessary. The current approach can be extended to future research using a different method, such as finite element grilling technique, mesh-free technique on reinforced concrete pavements or jointed concrete pavements.Originality/valueThe finite element approach adopted in this paper involves six degrees of freedom for each node. Furthermore, to the best of the authors’ knowledge, no prior study has done seven separate parametric investigations on the modal analysis of rigid pavement resting on two-parameter soil.

Vibration energy accumulation and absorption characteristics of pseudo acoustic black hole wedge

The Acoustic Black Hole (ABH) is an effective structure for harvesting and dissipating energy from flexural waves. It works by reducing the thickness of the ABH wedge in a power law relationship with m ≥ 2, which rapidly decreases the local phase velocity of flexural waves and leads to an energy convergence effect. However, the vibration performance may differ if the tapered wedge does not meet the requirements of a typical ABH. This article introduces and discusses two types of “pseudo-ABH” wedges: linear-degenerate ABH and step-degenerate ABH. These wedges do not follow the power-law and continuity conditions of typical ABH, respectively. To establish the dynamic models of pseudo-ABH wedges, the lumped-mass transfer matrix method (LTMM) and traveling wave analysis are introduced and validated using analytic solutions of the non-uniform one-dimensional Euler-Bernoulli beam and finite element method. Meanwhile, a good match between the results of the Timoshenko and Euler-Bernoulli beam theory also indicates the correctness of our model. The energy ratio and reflection coefficient are defined to characterize the energy accumulation effect and vibration absorption performance of the pseudo-ABH wedges. The vibration performance of the linear-degenerate ABH is closer to the typical ABH than the step-degenerate ABH. The step-degenerate ABH has more effective energy accumulation and reduction performance for individual frequencies. However, as the number of segments in the step-degenerate ABH increases, its dynamic performance becomes closer to that of the typical ABH. The novelty of this article is to study vibration energy accumulation and absorption characteristics of pseudo acoustic black hole wedges using LTMM model, disclose the differences of linear and step degenerate ABH for their performance, and recommend the step degenerate ABH in place of the typical ABH of a power law thickness relationship.

Yield design-based analysis of reinforced soil structures, making use of different models of reinforced soils

This contribution is aimed at applying the static and kinematic methods of the yield design theory, initially developed for homogeneous soils, to the stability analysis of reinforced soil structures. Several mechanical models of reinforced soils are considered to this end, starting from the mixed modelling approach which is the most intuitive one, according to which the reinforcements are treated as one-dimensional beam elements embedded in the soil regarded as a three-dimensional continuum. While this first model is posing some difficulties as regards the implementation of the lower bound static approach, a homogenization procedure should be preferred in the case of a dense array of regularly spaced inclusions, leading to the formulation of a macroscopic strength condition for the homogenized reinforced soil. Since the latter formulation, unlike the mixed modelling approach, fails to account for the shear and flexural strength characteristics of the reinforcements, a continuum multiphase description of reinforced soils, which may be considered as an extension of the previous homogenization method, has been developed. Such a multiphase model, which combines the advantages of the two previous models, is able to incorporate in an explicit way not only the shear and bending strength capacities of the reinforcements, but also a specific failure condition at the soil-inclusion interface. This contribution presents some illustrative applications of the yield design theory and related upper and lower bound methods to the design of typical reinforced soil structures, using the three above mentioned models.

Large deformations of hyperelastic curved beams based on the absolute nodal coordinate formulation

Compared with traditional linear elastic materials, the soft structure composed of incompressible hyperelastic materials has not only geometrical nonlinearity but also material nonlinearity during deformation. In this paper, the absolute nodal coordinate formulation (ANCF) is used to study the large deformations and large overall motions of incompressible hyperelastic curved beams. A novel large deformation dynamic modeling method for curved beams made of hyperelastic materials is proposed, in which a simplified Neo-Hookean model is combined with the one-dimensional ANCF beam element. The elastic force vector is calculated according to the exact expression of curvature. The dynamic equations are derived by using the virtual work principle. The dynamic responses of a cantilever silica gel beam under gravity are calculated based on the present method and compared with those of the improved low-order beam element (ILOBE), high-order beam element (HOBE), and commercial finite element analysis software (ANSYS). Simulation results show that the proposed method can accurately describe the large deformation and large overall motion of the beam, and has better computational efficiency. Research in this paper provides an efficient dynamic model for the dynamics analysis of soft robot arms.

Dynamic modeling of a fish tail actuated by IPMC actuator based on the absolute nodal coordinate formulation

Ionic polymer metal composite (IPMC) is a smart material with low driving voltage, high energy conversion, light weight and simple structure. It is suitable for driving the tail fin of small bionic fish. Actuators made of this material are quite flexible, and they are laborious to accurately describe the complex deformation of structures. Absolute nodal coordinate formulation (ANCF) has great merits in describing large deformation and large displacement problems. In this paper, the feasibility of ANCF in dynamic modeling of a fish tail actuated by IPMC actuator will be explored for the first time. The tail fin is simplified into two forms: a pure flexible IPMC beam and a hybrid beam that consists of an IPMC beam and a fixed rigid beam. The ANCF one-dimensional two-node beam element is adopted. Considering the influence of deformation curvature, the exact expression of generalized elastic force is obtained. The proposed dynamic model can describe the large deformation problem of the flexible beam. The dynamic responses of the pure IPMC beam tail fin and the hybrid tail fin driven by square wave voltage are calculated. The displacement changes of end nodes are compared, and the swing law under different driving voltage amplitude, frequency, and fluid resistance is analyzed. It is found that the driving efficiency of IPMC can be improved by increasing the driving voltage amplitude, reducing the voltage frequency, and reducing the fluid resistance in a certain range. This research would be beneficial to the study of the large swing motion mechanism of bionic robotic fish.

Development and Validation of an Active Muscle Simplified Finite Element Human Body Model in a Standing Posture.

Active muscles play an important role in postural stabilization, and muscle-induced joint stiffening can alter the kinematic response of the human body, particularly that of the lower extremities, under dynamic loading conditions. There are few full-body human body finite element models with active muscles in a standing posture. Thus, the objective of this study was to develop and validate the M50-PS+Active model, an average-male simplified human body model in a standing posture with active musculature. The M50-PS+Active model was developed by incorporating 116 skeletal muscles, as one-dimensional beam elements with a Hill-type material model and closed-loop Proportional Integral Derivative (PID) controller muscle activation strategy, into the Global Human Body Models Consortium (GHBMC) simplified pedestrian model M50-PS. The M50-PS+Active model was first validated in a gravity standing test, showing the effectiveness of the active muscles in maintaining a standing posture under gravitational loading. The knee kinematics of the model were compared against volunteer kinematics in unsuited and suited step-down tests from NASA's active response gravity offload system (ARGOS) laboratory. The M50-PS+Active model showed good biofidelity with volunteer kinematics with an overall CORA score of 0.80, as compared to 0.64 (fair) in the passive M50-PS model. The M50-PS+Active model will serve as a useful tool to study the biomechanics of the human body in vehicle-pedestrian accidents, public transportation braking, and space missions piloted in a standing posture.

P19. Effect of stature and lordosis on vertical falls in the female lumbar spine

P19. Effect of stature and lordosis on vertical falls in the female lumbar spine

Optimization of Continuous Fiber Path Planning for an Additively Manufactured Open-Hole Specimen

This study presents a numerical method for optimizing the quantity and the placement of reinforcements along the principal-stress trajectories. The model representing carbon fiber composite structures consists of solids and embedded one-dimensional beam elements. Based on the Runge-Kutta method, the reinforcing structure is optimized considering the manufacturability of additive manufacturing (AM). For a case study, the optimization method is performed on an open-hole specimen. The Young’s modulus and the tensile strength of the optimized structure show an increase of more than 30 % and ~50 % in the simulation, respectively, compared to the reference specimen from another study. Robotic additive manufacturing is used to fabricate the specimen for experimental validation. The prediction of absolute values of tensile strength are reliable comparing to the experimental test, however, there is a deviation of more than 30 % in the linear-elastic behavior possibly due to the presence of voids in the printed part.

Efficient elastic stress analysis method for piping system with wall-thinning and reinforcement

A piping system stress analysis need to be re-performed for structural integrity assessment after reinforcement of a pipe with significant wall thinning. For efficient stress analysis, a one-dimensional beam element for the wall-thinned pipe with reinforcement needs to be developed. To develop the beam element, this work presents analytical equations for elastic stiffness of the wall-thinned pipe with reinforcement are analytically derived for axial tension, bending and torsion. Comparison with finite element (FE) analysis results using detailed three-dimensional solid models for wall-thinned pipe with reinforcement shows good agreement. Implementation of the proposed solutions into commercial FE programs is explained.

Inclined composite guardrails/safety barriers – Numerical and experimental evaluation of their transverse stiffnesses and compliance with standards

Three-point flexure and axial torsion tests were undertaken to establish the longitudinal elastic flexural and in-plane shear moduli of pultruded GFRP tubes. They were used to define one-dimensional two-node beam elements for modelling single- and two-bay inclined guardrails with inclinations up to 60°. Subsequently, three-dimensional FE models were developed to analyse more accurately single- and two-bay 30° inclined guardrails. The results from these analyses were compared with those of full-scale load tests on 30° inclined guardrails subjected to transverse normal preload, usability, and ultimate loads applied to the handrails. It is shown that the analysis results based one-dimensional elements significantly underestimate the mean handrail deflections and over-estimate the guardrails’ transverse stiffness. By contrast, using three-dimensional elements in the FE models give more accurate predictions, with mean handrail deflections 9% and 14–16% lower than single- and two-bay test values respectively. The corresponding percentages for mean transverse stiffnesses are 10% and 12.5 – 14.3% higher respectively. It was also observed that the responses of the guardrails were linear, the residual deflections on unloading were less than permitted for the preload, usability and ultimate loads. Furthermore, neither the single- nor the two-bay 30° inclined guardrails sustained any damage.

Conformal Wireframe Nets for Trimmed Symmetric Unit Cells in Functionally Graded Lattice Materials

Tessellating a periodic unit cell of lattice material to fill a design space in complex geometries has many challenges arising from their computer-aided design (CAD) modeling intricacy. A solution to this difficulty is the use of trimmed micro-truss lattice structures with a conformal net. This paper presents a novel algorithm for constructing conformal lattice net as wireframe of one-dimensional line segments suitable for Bravais cubic symmetric truss-based topologies. The novel algorithm is an excellent candidate when dealing with lattice structures using cubic, body-centered cubic (BCC), face-centered cubic (FCC), and/or diamond unit cell configurations. The wireframe structure is easily transferred into one-dimensional beam elements for microscale optimizations to obtain a functionally graded lattice material. It is shown that introduction of the lattice net resulted in a significant reduction in the mass of the optimized design.

Microfluidic microcantilever as a sensitive platform to measure evaporation rate of picoliters of ethanol

Resonating microfluidic cantilevers are used for a broad range of biochemical sensing applications where a shift in the resonance frequency is used to detect minute changes in the cantilever mass. These multifunctional microfluidic microcantilevers open up opportunities for new ultrasensitive biochemical sensors wherein the target species in a carrier fluid bind to the inner functionalized walls of microfluidic channel, thereby changing the mass and hence the resonance frequency of the system for detection. In this paper, we develop computational models that predict the change in the resonance frequency as a function of change in mass for this hollow microcantilever system. We present computational models to simulate this process and validate the models using experimental data based on the evaporation of ethenol, a commonly available volatile compound. Specifically, a computational approach is presented in two variants; a one-dimensional structural beam element model, and a three-dimensional finite element model. The numerically predicted increase in the resonance frequencies due to a decrease in ethanol mass correlates well with experimental data. The models enable the determination of proof-of-concept and the rational design of novel resonant-based microfluidic microcantilever systems.

One-dimensional finite element analysis of thin-walled box-girder bridge

Presented herein is a finite element approach for the static analysis of thin-walled box-girder bridge subjected to Indian railway loading using a three-noded one-dimensional beam element. The one-dimensional model is favoured over the three-dimensional model due to its simplicity and cost-effectiveness during the initial design and analysis phase of the box-girder bridge. The complex structural actions of thin-walled box-girders such as torsional warping and cross-sectional distortion are taken into consideration in addition to extension, bending and torsion. Keeping in mind these complex actions, the beam element incorporates three extra degrees of freedom in addition to the familiar six degrees of freedom per node. MATLAB coding is done to obtain various response parameters for single as well as double cell box girders. Furthermore, the variation of different response parameters due to changes in radius, span length, load position, varying cross-section and various combinations of Indian rail loads has also been studied. The finite element approach used in this study is validated by solving two numerical examples which are in excellent agreement with the results of previous studies.

A New Conceptual Modelling Method for Vehicle Subframe to Evaluate Dynamic Performance of Structures at Conceptual Design Stage

In recent years, the reduction of noise and vibrations caused by the road or internal components of vehicles have been a significant factor in the satisfaction and comfort of the occupants of cars. Therefore, to minimize these vibrations, the dynamic behaviour of the components of the vehicle should be considered in detail to reduce their level by setting useful parameters on structures. Nowadays, the conceptual model method can be regarded as a suitable alternative to the fundamental sophisticated computational techniques in measuring the vibration of vehicle components. Accordingly, the advanced finite element (FE) model examined for the subframe structure under the vehicle engine, and its conceptual model is developed by the one-dimensional beam elements to justify the dynamic behaviour of the subframe. The results of the experiments in the laboratory as well as the advanced subframe model are adapted, and the integrity of the natural frequencies and the mode shapes at low frequencies represented comprehensively. The result of the subframe concept model compared to the experimental model and computer-aided-engineering (CAE) model showed that the modal assurance criterion (MAC) is above 0.75 for the first four mode shapes of subframe structure and is above 0.9 for first and fourth mode shapes, and also the error percentage of natural frequency is lower than 8%. Therefore, for the analysis of the subframe performance in noise, vibration, and harshness (NVH) domain, the presented model could be considered in the conceptual phase design to reduce the solution time significantly.

Equivalent beam modeling scheme based on three-dimensional structure with blade element concept

The most important step in the design of wind turbine and blades is integrated load analysis, which is usually designed to describe a three-dimensional structure using a one-dimensional beam element; represents a three-dimensional blade with aerodynamic and structural information. In this regard, one-dimensional elements are required to accurately represent all the structural properties of a three-dimensional component. Most of the previous methods regarded the blade as a linear structure, resulting in limitations associated with nonlinearities. The geometry of the blades has a significant change along the length, and the composition of the materials used inside the blades is very complex, so these methods are not suitable for extracting the characteristics of the blades. In this paper, a new design scheme of a one-dimensional beam modeling method is proposed based on the blade sectional element concept that is easier and faster to apply without performing nonlinear analysis. In addition, the validation of the accuracy of its numerical analysis results, the total mass and modal analysis results are compared between three-dimensional blade and one-dimensional blade.

Effect of Shear Connector Layout on the Behavior of Steel-Concrete Composite Beams with Interface Slip

In a steel-concrete composite beam (hereafter referred to as a composite beam), partial interaction between the concrete slab and the steel beam results in an appreciable increase in the beam deflections relative to full interaction behavior. Moreover, the distribution type of the shear connectors has a great impact on the degree of the composite action between the two components of the beam. To reveal the effect of shear connector layout in the performance of composite beams, on the basis of a developed one-dimensional composite beam element validated by the closed-form precision solutions and experimental results, this paper optimizes the layout of shear connectors in composite beams with partial interaction by adopting a stepwise uniform distribution of shear connectors to approximate the triangular distribution of the shear connector density without increasing the total number of shear connectors. Based on a comparison of all the different types of stepped rectangles distribution, this paper finally suggests the 3-stepped rectangles distribution of shear connectors as a reasonable and applicable optimal method.