Planar Finite Element Model Research Articles

Cross-sectional zero-dimension temperature model for thin-walled circular tubes in space environment

A sufficiently accurate, yet computationally efficient prediction of temperature field is essential for design of spacecraft structures. This paper presents a model dimension reduction method for thermal analysis of thin-walled circular tubes in space environment, which takes into account radiation heat transfer among the internal surfaces besides heat conduction along the circumferential direction and radiative emission from the external surface. Temperature distribution on the tube cross section is approximated by a series of harmonic functions, so that a one-dimensional problem is reduced to that of zero dimension. The relation between average and perturbation temperatures that depend only on time is broadened to fully coupled one. By comparison to the previous model and the plane finite element model, the accuracy and economy of the new model are illustrated. The results show that internal radiation exchange plays an important role in thermal analysis of thin-walled circular tubes used extensively in spacecraft appendages. Furthermore, differences between present and previous models are analyzed and a two-way analysis of variance is performed to determine the effect of various physical and geometric parameters on the temperature distribution and response of the tubes. The work can be further developed to analyze thermally induced deformation and vibration of spacecraft structures.

The use of planar and three-dimensional calculation models for the numerical modeling of retaining walls in conditions of dense urban construction

In modern realities, the construction of multi-story buildings increasingly has to be carried out in the conditions of dense urban development. Since high-rise buildings are characterized by the presence of deep pits, there is a need to select the parameters of the enclosing structures (retaining walls) and take into account the influence of the pit arrangement and enclosing structures on the existing building. Numerical simulation of the stress-strain state (SSS) of the elements "soil base - existing structures - pit enclosure" was performed to assess the impact of choosing the dimensions of the calculation scheme when designing a deep pit and assessing its impact on existing buildings and selecting effective parameters of enclosing structures. with different dimension options (flat two-dimensional and spatial three-dimensional) calculation scheme. Modeling was performed using the finite element method using a nonlinear model of soil deformation in the Plaxis software package. Since the soil conditions within the construction site are complex (the presence of a significant layer of plastic and flowing clay soils and powerful aquifers), the level of groundwater within the construction site was taken into account in the modeling and the effect of water lowering during the development of the pit was modeled accordingly for a more correct assessment of the stress-strained state of pit enclosure elements and the impact on existing structures. Numerical calculations of retaining walls provide for taking into account the technological sequence of the construction of retaining walls and modeling of the step-by-step development of the pit. Studies have shown that the use of a spatial finite-element model of the system "soil base - existing structures - pit enclosure" provides an opportunity to more correctly and effectively assess the stress-deformed state of system elements due to taking into account the spatial rigidity of the elements of the pit enclosure and the foundations of existing structures. The values of the displacements of the retaining walls obtained by the calculation of the spatial finite element model (FEM) are 20% smaller than the values obtained using the plane FEM. The values of the bending moments obtained by the calculation of the spatial FEM are 10% smaller than the values obtained using the plane FEM.

Study on Damage Inference of Parker Trusses Based on Bayesian Principles

The assessment of the health condition and safety of engineering structures is currently a research focus in the field of civil engineering. The traditional deterministic model for damage recognition is limited by the fine reading of field inspections and the accuracy of experts, resulting in a low recognition rate. Structural damage identification methods that consider uncertainty have been developed due to modelling errors, observation noise, system time variability, and other factors that lead to uncertainty. This study focuses on the Parker truss structure, and a two-dimensional planar finite element model is established by setting various key parameters such as prior distribution, stiffness, modulus of elasticity, node distribution, and external loading. The model is updated using the Bayesian updating principle. This principle is then combined with the finite element model. Opensees software is used for programming, and the Monte Carlo random sampling technique is used for structural damage inference. The study results demonstrate that the method can accurately identify the damage level of Parker truss structures with high robustness. The method can be of reference significance and practical value for identifying damage in truss structures.

Influence of near‐field ground motions with fling‐step and forward‐directivity characteristics on seismic response of stilted buildings in mountainous area

SummaryNear‐field ground motions with fling‐step and forward‐directivity characteristics contain large‐amplitude pulses in velocity history, causing severe damage to stilted buildings in mountainous areas. In this study, three groups of 20 near‐field ground motions with fling‐step and forward‐directivity characteristics and 10 far‐field ground motions were selected as seismic inputs. Nonlinear response history analysis (NLRHA) was performed on plane finite element models of two seven‐story stilted frame structures, one with steel braces in the stilted story and the other without steel braces in the slope direction. Structural seismic response obtained from NLRHA was discussed in terms of inter‐story drift ratio (IDR) and peak floor acceleration (PFA). In addition, damage to two structures was assessed using the modified Park–Huang damage model. The results show that stilted structures exhibit greater inter‐story ratios and damage index values under near‐field ground motions with fling‐step characteristics and forward‐directivity characteristics than far‐field ground motions, where the stilted story has the highest amplification ratio in both IDR and damage index among floors. Designers should pay sufficient attention to the influence of ground motions with fling‐step and forward‐directivity characteristics on seismic demands and damage to stilted structures. The peak inter‐story ratio and damage index of stilted structures with steel braces were significantly lower than that of stilted structures without braces, proving the validation of setting steel braces on reducing the seismic demands of stilted structures and improving structural seismic safety. Additional NLRHA performed using artificial pulses shows that the seismic response of stilted buildings is related to pulse periods of near‐field ground motions and the greatest seismic demands and damage are obtained when the pulse period is 1.5–1.6 times the fundamental period of the stilted building.

Fast tooth deflection calculation method and its validation

For the development of high power density gearboxes the knowledge of the gear mesh behavior is important. Especially, the tooth deflection influences flank load distribution and is the basis for the design of flank modifications. Analytical and numerical approaches are suitable to evaluate the behavior. Since numerical methods are complex, elaborate and time-consuming, fast and accurate analytical methods are still important and are worth to be further developed and assessed.An analytical method for calculating tooth deformation for gears goes back to Weber and Banaschek from 1953. In the initial work the final equations are given without many intermediate steps in the plane strain assumption for materials with Poisson’s ratio ν = 0.3. This paper derives the tooth deflection equations in a more detailed and general manner for any linear material. The final equations are valid for the plane stress and plane strain state in one new closed representation and are therefore suitable for an efficient implementation. While the plane strain state is typical for gears, the plane stress state is significant for a thin slice model or special gearings. The presented method captures the shear influence with a more detailed calculation of the shear correction factor.A calculation study validates the results from the derived analytical tooth deflection calculation method with a plane Finite Element Model. In the study the point of application of force and the gear body are varied to cover the influence of different variants (size and mesh position). Finally limits of the analytical modeling and the validation are discussed.

Optimization design of metamaterial vibration isolator with honeycomb structure based on multi-fidelity surrogate model

The hexagonal periodic structure of the honeycomb is a magic product of nature and shows great mechanical potential. In this work, a type of metamaterial vibration isolator with a honeycomb structure is proposed. The strain, deformation, and natural frequency of the vibration isolator are calculated by the two-dimensional plane finite element model and the simulation accuracies are validated by the experiments. As the design of the metamaterial vibration isolator involves time-consuming finite-element simulation, a multi-fidelity sequential optimization approach based on feasible region analysis (MF-FA) is proposed. In the proposed method, the refined and coarse mesh models are developed as the high- and low-fidelity models, and a two-phase multi-fidelity updating strategy is carried out. In the first phase, sample points are added to the constraint boundary to find the feasible solution quickly, in the second phase, the quality of the feasible optimization solution is gradually improved in the feasible region until it converges to the global optimal solution. Finally, the optimized metamaterial vibration isolator is manufactured and its superiority is validated. Results illustrate that the proposed approach can obtain a desirable optimum, whose natural frequency error between the experimental and the expected value is improved by 12.67% compared with the initial design.

An investigation into the moving load problem for the lifting boom of a ship unloader

While the moving load problem has received a lot of attention in the context of bridges traversed by road or rail vehicles, the same cannot be said about ship unloaders where research is limited and typically focused on displacements. In ship unloaders, the moving system is composed of a trolley, attached grab, and payload. The interaction between the moving system and the lifting boom on which the trolley travels can lead to high stresses. Given that the stress ranges and associated number of cycles experienced by a section of the lifting boom determine its fatigue life, these stresses must be assessed as accurately as possible. For this purpose, dynamic transient analysis of the effects of a payload-carrying trolley moving along the boom is carried out using an equivalent planar finite element model. Results show how bending stresses are affected by the inertial forces of the structure and the moving load, the ratio of the mass of the load to the mass of the boom, the flexibility of the moving system, and the payload mass and its swing angle.

Benchmarks for Accelerated Cyclic Plasticity Models with Finite Elements

In numerical simulations of components subjected to low-cycle fatigue loading, the material cyclic plasticity behavior must be modelled until complete stabilization, which occurs approximately at half the number of cycles to failure. If the plastic strain per cycle is small, a huge number of cycles must be simulated, which results into a huge and thus unaffordable simulation time. Acceleration techniques for shortening this time are useful, although their accuracy needs to be checked. This work aims to compare different approaches (nonlinear kinematic with “initial” and “stabilized” parameters and combined nonlinear kinematic and isotropic with the speed of stabilization fictitiously increased). It considers two benchmarks taken from the literature, in which the material has opposite cyclic behaviors (hardening, softening). A plane finite element model can be used in both benchmarks, thus permitting a simulation up to complete stabilization. Results confirm that the common approach of considering only the kinematic model (calibrated on “initial” or “stabilized” material state) from the very first cycle could lead to relevant errors. The acceleration technique based on a fictitious increase in the speed of stabilization leads to accurate results. Guidelines for calibrating this technique on a material’s hardening or softening behavior are, finally, proposed.

Automatic prediction of the fatigue crack trajectory in plane finite element models

A module for automatic prediction of the fatigue crack trajectory in plane finite-element models in Ansys APDL software package was developed. Crack propagation is modeled by exclusion of elements from the active set in the direction, which is determined based on criterion of the maximum energy flux to the crack tip. The module determines the parameters of fracture mechanics (stress intensity factor and J-integral) at each step of crack propagation.

In-plane elastic flexibility of cross laminated timber floor diaphragms

No appropriate method exists to calculate the in-plane flexibility of Cross Laminated Timber as a floor diaphragm. This flexibility affects the load distribution between shear walls, bracing or cores, as well as adding to local deflections and inter-storey drift. This paper presents a sensitivity analysis based on experimentally measured connection behaviour from the literature and the present study. An important new contributing factor is described: the connection of the floor panels to the supporting wall panels below allows the walls to act as top and bottom chords in the bending and shear of the panel. A new equivalent frame model is described to capture the significant mechanisms of deformation of the diaphragm, validated against a planar finite element model of the elastic behaviour of the panels and the connections between them. The low computational cost of the simplified model allows a wide sensitivity analysis to be carried out, and also makes it suitable for practical design calculations. The flexibility of the floors studied here was seen to be dominated by the slip between panels, rather than panel rotation or bending of the panels themselves. The supporting walls have a strong influence on the moment distribution, but do not strongly influence the slip between panels.

Finite Element Analysis of Extrusion Force and Work Characteristics of ECAP

A planar finite element model is created for modeling the equal channel angular pressing (ECAP) processing of copper, by which the technological parameters can be determined for different initial parameters of the ECAP process. The structure of the model is described, as well as the extraction of the force and work data, furthermore results for the effect of the initial parameters, e.g. the friction and the frictional model on the extrusion force and work characteristics are shown.

Research on composite bending stress of asymmetric gear in consideration of friction

Compared with the conventional gear, the asymmetric gear has better root bending stress and tooth contact stress. Taking a pair of asymmetric involute spur gears as the research object, a model of asymmetric gear considering the influence of friction and shear stress on root bending stress is established. Take the upper boundary point of single tooth meshing area as example, the formula for calculating root bending stress of asymmetric gear is deduced under friction, get the rule of root bending stress without neglecting the friction force and the shear stress by MATLAB. At the same time, we design the plane finite element model of conventional gear (20°/20°) and asymmetric gear (20°/35°) by using APDL. The upper and lower boundary points of the double tooth meshing area, the upper and lower boundary points of the single tooth meshing area, the meshing node are systematically studied, get the change rules of root bending stress in the meshing process under the condition that the friction force cannot be ignored.

Finite Difference Method in Stress Analysis of Anchorage Zone of Highway Extradosed Cable Stayed Bridge

With the development and wide application of extradosed cable stayed bridge, an effective method is needed for simulation of the stress distribution in anchorage zone, which plays a vital role in transferring force from the cable to the pylon and diverting the cable direction. Based on the Finite Difference Method (FDM), an efficient and practical method of stress filed simulation was presented in the paper. First, a plane finite element model was established using ABAQUS, to determine the boundary condition for FDM. Based on this, FDM was used to simulate the stress distribution of the concrete in the anchorage zone. Finally, on the simulation result was calculated and in comparison with finite element model result. It has been found that: The vertical compressive stress of concrete in the anchorage zone gradually reduces from the middle to the two sides, and the stress assumes double peak type in transverse. Compared with the finite element solutions, the approximate solution simulated by FDM improve the computational efficiency with certain accuracy keeping, except the loading area. In vertical orientation, the concrete in the place of H (the width of the pylon) from cable force acting position is in a state of uniform stress.

Analysis of thermal behavior on concrete box-girder arch bridges under convection and solar radiation

The two-dimensional finite element method can be used to calculate the thermal field distribution of prestressed concrete bridge girders. However, this method is not appropriate for the concrete box-girder arch bridges, because they have different azimuth and dip angles at the top and bottom flanges along arch axis. Thus, an experimental and analytical study was conducted on a concrete box-girder arch bridge located in Guizhou, China, to investigate the thermal behavior under convection and the solar radiations. To determine the vertical temperature gradients, a two-dimensional plane finite element model was used to calculate the thermal field based on meteorological parameter methods. In addition, the three-dimensional beam finite element model was proposed to study the thermal stress and displacement of arch bridges using the vertical temperature gradients. Finally, the thermal behavior of the concrete box-girder arch bridges determined by the two-dimensional plane and three-dimensional beam finite element model was verified by three-dimensional solid finite element model.

Two dimensional modeling of helical structures, an application to simple strands

Herein, we elaborate a generic, planar finite element model for the simulation of the mechanical response of helical structures to axial and torsional strain. We verify the modeling approach over a wide range of helix angles using closed-form expressions. Thereafter, we present a case study application addressing the structural response of single layer engineering strands. Finally, we analyze the model’s computational merits.

Finite element implementation of a varied friction model applied to torsional fretting wear

Coefficient of friction is a significant factor for investigating stress and strain on the contact surface for a problem on torsional fretting wear. First, in this paper, a variable coefficient of friction model related to space and time is introduced. The evolution of friction coefficient is governed by the local contact history and the slip distance. Then, this model is implemented in the finite element code ABAQUS by the user subroutine FRIC. A sphere–plane finite element model is constructed to simulate stress and strain on the contact surface under the torsional fretting loading. Comparisons between the experimental friction torque curves and the numerical data rooting from this model show a good agreement. In view of the relation between the plastic strain and friction shear stress, it is seen that damage mechanisms in the different slip regimes are different. Finally, crack initiation location in the mixed slip regime is predicted based on the Smith–Watson–Topper multiaxial fatigue criterion. The predicted results are in agreement with the corresponding experiments.

Mechanics Characteristics of Expressway Tunnel Through Fault Fracture Zone at the Entrance

Guandoushan tunnel in the Yibin - Luzhou expressway passes through fault fracture zone at the entrance. Structure internal force are complex during or after the construction. It challenges the safety during construction and operation. Plane finite element model was used to calculate internal force of primary support in the cases of different buried depths and three dimensional finite element model was applied to calculate stress distribution of primary support and secondary lining of the tunnel through fault fracture zone. The results indicate: with the increasing of buried depth, the loads acting on the structure will increase. It leads to uneven stress distribution in longitudinal direction, especially in the border of fault zone. It is suggested to increase the longitudinal reinforcement to improve overall longitudinal shearing resistance capacity and set deformation joint in the intersection to strengthen the longitudinal deformation ability of structure.

Use of Orthogonal Arrays for Efficient Evaluation of Geometric Designs for Reducing Vibration of a Non-Pneumatic Wheel during High-Speed Rolling

Abstract During high speed rolling of a nonpneumatic wheel, vibration may be produced by the interaction of collapsible spokes with a shear deformable ring as they enter the contact region, buckle, and then snap back into a state of tension. In the present work, a systematic study of the effects of six key geometric design parameters is presented using Orthogonal Arrays. Orthogonal Arrays are part of a design process method developed by Taguchi which provides an efficient way to determine optimal combinations of design variables. In the present work, a two-dimensional planar finite element model with geometric nonlinearity and explicit time-stepping is used to simulate rolling of the nonpneumatic wheel. Vibration characteristics are measured from the FFT frequency spectrum of the time signals of perpendicular distance of marker nodes from the virtual plane of the spoke, and ground reaction forces. Both maximum peak amplitudes and RMS measures are considered. Two complementary Orthogonal Arrays are evaluated. The first is the L8 orthogonal array which considers the six geometric design variables evaluated at lower and higher limiting values for a total of eight experiments defined by statistically efficient variable combinations. Based on the results from the L8 orthogonal array, a second L9 orthogonal array experiment evaluates the nonlinear effects in the four parameters of greatest interest, (a) spoke length, (b) spoke curvature, (c) spoke thickness, and (d) shear beam thickness. The L9 array consists of nine experiments with efficient combinations of low, intermediate, and high value levels. Results from use of the Orthogonal Array experiments were used to find combinations of parameters which significantly reduce peak and RMS amplitudes, and suggest that spoke length has the greatest effect on vibration amplitudes.

Finite elements prediction of thermal stresses in work roll of hot rolling mills

A simplified numerical approach based on finite elements to compute thermal stresses occurring in work roll of hot rolling mills is here proposed. To decrease both the complexity of the analysis and the computational effort, this approach implements a plane finite element model of the work roll alone, loaded on its surface by the rotating thermal actions due to the cyclic sequence of the conductive heating caused by the contact with hot strip and cooling provided by water jets. Results from thermal analysis are preliminary compared to an analytical solution available in the literature and then applied as thermal input in the subsequent mechanical finite elements simulations, which provide thermal stress in the work roll and the elastic-plastic evolution of elements, close to the work roll surface.

A planar finite element model of bolus containment in the oral cavity

As individuals age, one of the objective changes that occurs in the oropharyngeal swallow is the development of a delay between bolus entry into the pharynx and the initiation of airway protection mechanisms. For longer delays, this phenomenon is sometimes referred to as “premature spillage,” and it has been suggested that such spillage, which is a risk factor for dysphagia, may be associated with pre-swallow lingual gestures, or “tongue pumping.” The goal of the current study was to develop a simplified two-dimensional computational model of the oropharynx to simulate the containment of a Newtonian fluid bolus within the oral cavity in response to a given pattern of lingual gestures for different viscosities. An arbitrary Lagrangian–Eulerian simulation was performed using the commercial finite element software package, LS-Dyna. It was found that for a given lingual motion, higher viscosity Newtonian boluses, consistent with those offered therapeutically, were able to be contained within the simulated oral cavity while a lower viscosity bolus would be “spilled,” suggesting a potential mechanisim by which thickened liquids may reduce aspiration. Although the current data must be validated with more realistic, three-dimensional geometric information and for a wider range of bolus rheologies, they represent an exciting first step towards realistic modeling of oropharyngeal bolus flow.