Shell Element Model Research Articles

Behaviour and design of fixed‐ended steel equal‐leg angle section columns

AbstractThe mechanical behaviour and design of fixed‐ended steel equal‐leg angle section members subjected to axial compression are addressed in this study. First, the critical buckling behaviour is described. Experimental data on steel equal‐leg angle section columns collected from the literature are then used for the validation of numerical (shell finite element) models, developed within the commercial package ABAQUS. Validation is performed by means of comparisons between the test and numerical results, considering ultimate loads, failure modes and the load‐deformation responses, all of which are shown to be generally in good agreement. A numerical parametric study is then presented considering steel angle section columns with a wide range of slenderness values. The behaviour and load‐carrying capacity of the columns is shown to be dependent on, not only the column slenderness, but also the ratio of the elastic torsional‐flexural buckling load to the elastic minor‐axis flexural buckling load. Finally, the collected experimental and generated numerical results are used to develop a new design approach for fixed‐ended steel equal‐leg angle section columns, reflecting the observations made. The proposed approach offers improved accuracy and consistency in strength predictions compared to the existing codified design rules.

Investigation on Failure Mechanisms of Symmetric and Asymmetric Cellular Steel Beams

AbstractThe investigation on non‐composite asymmetric cellular beams is limited. Previous research focused on the behavior of asymmetric steel cellular sections by using different root beam for the top tee and the lower tee section. Moreover, asymmetric beams can be designed in different concepts as in the case of this study where the same root beam is used for top and bottom tee of the non‐composite asymmetric cellular beams. This research presents a numerical study on the structural behavior and resistance of symmetric and asymmetric non‐composite cellular steel beams using IPE sections. Five cellular steel beams were analytically modeled and verified using experimental work from published research. The study was carried out using three‐dimensional finite shell element modeling of I‐shaped cellular steel beams with a broad spectrum of cross‐sectional dimensions, unrestrained lengths, web perforation configurations, application of loads and various steel grades. Geometrical and material nonlinear analysis was performed by using ABAQUS software. The results of asymmetric sections showed notable improvements on the small parent sections failing under vierendeel mechanism while the results for the deeper sections showed the opposite.

Lateral‐Torsional Buckling of beams with warping restraints at Supports

AbstractIn practice, the elastic lateral‐torsional buckling of doubly symmetric I‐section steel members is analyzed assuming free warping at supports. However, welded stiffeners, bolted end‐plate connections or column base plates maintain elastically the opposite flange out‐of‐plane rotations and thus induce substantial warping restraints.This paper proposes analytical formulations for the evaluation of the elastic critical bending moment for lateral‐torsional buckling of beams taking into account warping restraints at supports. Assuming series of displacement and rotation fields containing one or two terms, the energy method permits to derive expressions of the critical bending moment under constant and linear distribution of the bending moment. A single expression of the warping coefficient kw is proposed whatever the shape of the bending moment diagram. The factor C1 can be conveniently calculated by multiplying two coefficients that depend on the shape of the bending moment diagram and on the warping restraint stiffness, respectively.Finite Elements analyses of beams with warping restraints at supports have been performed considering a beam element model developed with LTBeamN and a shell element model created in ANSYS. The analytical model is in good agreement with the numerical results obtained by the two finite element models.

Vibration characteristics of plates and shells with functionally graded pores imperfections using an enhanced finite shell element

The novelty of the current study is the development of an enhanced finite shell model using the first order shear deformation theory (FSDT) to study the vibration characteristics of imperfect functionally graded (FGM) plates and shells including porosities. Unlike standard (FSDT) theory, the proposed model presents an improvement of the FSDT via the introduction of a quadratic shear function allowing the exact representation of the parabolic distribution of the shear strains and avoiding the utilization of shear correction factors which are computationally costs. The finite element method is used for the discretization of the equations of motion and the assumed natural transverse shear strain (ANS) method is employed to avoid shear locking problems. The effect of porosity parameter and its distributions, namely even and uneven forms, is investigated through different numerical illustrative examples. The present finite shell element model provides better agreement with exact solutions in comparison by other theories. Finally, effects of different factors on vibrational behavior of imperfect FGM porous plates and shells are examined in detail.

The simulation of thermal deformation on lightweight optics with thick coatings

Lightweight optics utilized in high-power laser system can dissipate heat better and reduce system weight. Dielectric films can be designed for laser pulse modulation, high reflect rate and wide bandwidth. However, the deformation caused by coating residual stress will be large due to the large thickness of dielectric films and low stiffness of lightweight mirror, which brings a large bending deformation with the temperature variation. The traditional surface compensation technology is double-sided coating, but it is not suitable for lightweight mirrors. In this study, we construct a finite shell-element model to estimate the surface shape error caused by dielectric film coating residual stress on a lightweight mirror for surface pre-processing. Thermal deformation and bimetal effect deformation are also simulated.

A traction force approach for fatigue assessment of complex welded structures

AbstractA new traction force approach (TFA) for weld root fatigue analysis of complex cruciform connections is introduced. The approach defines the local nominal weld stress by using a solid element model and connecting the welded parts only from the toe and root lines. This enables the peak weld forces to be distinctly defined. The TFA approach was validated with a fully connected solid element model. As a comparison, the same analyses were performed for a shell element model. The study shows that the approach that is introduced here gives a good estimate for the local weld force with a maximum error of 10% while the commonly used shell element model greatly overestimates the peak weld force, particularly for complex connections. The analysis of fatigue‐tested connections showed that by using TFA, instead of an approach based on overall nominal weld stress, the scatter range index is reduced from 3.71 to 1.98. The TFA approach is much more efficient compared to conventional approaches because of the low pre‐ and post‐processing effort.

On the Modeling of Anisotropic Fiber-Reinforced Polymer Flange Joints

Abstract Fiber-reinforced plastic composite flanges have recently experienced a spectacular development in the area of pressure vessels and piping. The current procedures used for the design of these flanges are a major concern because of their inappropriateness to address the anisotropic behavior of composite materials. The current ASME code section X related to the design procedure of composite flanges uses the same analytical method as that of section VIII division 2, which treats the flanges as isotropic materials such as metallic flanges. This study deals with Fiber-reinforced plastic (FRP) bolted flange joints integrity and bolt tightness. A new developed analytical FRP model that treats anisotropic flanges with and without a hub is presented. The model is based on the anisotropy and a flexibility analysis of all joint elements including the gasket, bolts, and flanges. It is supported experimentally with tests conducted on a real NPS 3 class 150 WN FRP bolted flange. Furthermore, three different numerical models based on three-dimensional anisotropic layered shell and solid element models were conducted to further compare and verify the results obtained from the new developed analytical approach. The results show that the new model has potential to be used as an alternative tool to FEM to analyze the stresses and deformation of problematic FRP bolted joints.

Numerical Simulation and Design of Steel Angle Section Columns

The stability and design of fixed-ended stainless steel equal-leg angle section members subjected to axial compression are studied herein. Existing experimental data on stainless steel equal-leg angle section columns collected from the literature are used for the validation of numerical (shell finite element) models, developed within the commercial package ABAQUS. Validation is performed by means of comparisons between the test and numerical results, considering ultimate loads, failure modes and the load-deformation responses, all of which are shown to be generally in good agreement. A numerical parametric study is then presented considering angle section columns in the three main families of stainless steel (austenitic, ferritic and duplex) with a wide range of slenderness values. The behaviour and normalised load-carrying capacity of the studied members is shown to be dependent on not only the column slenderness, but also the ratio of the elastic torsional-flexural buckling load to the elastic minoraxis flexural buckling load. Finally, a design approach recently proposed for carbon steel angle section columns is extended for application to stainless steel and verified against the experimental and numerical results. The proposed approach offers substantially improved accuracy and consistency in strength predictions compared to the existing codified design rules.

Simulation analysis of mechanical properties of composite materials

Based on the technical study of a composite vertical tail, the mechanical properties of honeycomb sandwich structure at the leading edge of the composite were studied fundamental computational analysis. The stress calculation and modal analysis of sandwich beam/plate structure are carried out by using engineering algorithm and two finite element modeling methods. The comparative analysis of the results shows that the two modeling methods can effectively simulate the mechanical properties of composite sandwich structure. In the actual analysis of complex structures, a simple 2D shell element modeling method can be used for preliminary simulation analysis.

Experimental and numerical study of notched SHS made of different S355 steels

This study compares the mechanical behaviour of square hollow sections (SHS) made of three different types of S355: cold-formed, hot-rolled and offshore steel. A material model and failure criterion for each steel type were calibrated based on quasi-static uniaxial tensile tests. The failure criterion applies a recently proposed through-thickness damage regularisation model with the purpose of accurately describing the load-bearing capacity using shell elements. Experimental three-point bending tests were conducted at both quasi-static and dynamic conditions. Notches were used to trigger failure in the tests. The cold-formed steel exhibited the highest yield stress of the three steel types, while the offshore steel displayed better ductility than the other two. The numerical simulations showed that a shell element model of the SHS incorporating the regularisation scheme was able to describe the material behaviour and predict failure.

Behaviour and design of fixed-ended steel equal-leg angle section columns

The mechanical behaviour and design of fixed-ended steel equal-leg angle section members subjected to axial compression are addressed in this study. First, the critical buckling behaviour is described. Experimental data on steel equal-leg angle section columns collected from the literature are then used for the validation of numerical (shell finite element) models, developed within the commercial package ABAQUS. Validation is performed by means of comparisons between test and numerical results, considering ultimate loads and failure modes, all of which are shown to be generally in good agreement. A numerical parametric study is then presented considering steel angle section columns with a wide range of slenderness values. The behaviour and load-carrying capacity of the columns is shown to be dependent on, not only the column slenderness, but also the ratio of the elastic torsional-flexural buckling load to the elastic minor-axis flexural buckling load. Finally, the collected experimental and generated numerical results are used to develop a new design approach, suitable for incorporation into future revisions of Eurocode 3, for fixed-ended steel equal-leg angle section columns, reflecting the observations made. The proposed approach offers improved accuracy and consistency in strength predictions compared to the existing codified design rules. The reliability of the new design approach, with a recommended partial safety factor γM1 = 1.0, is verified following the EN 1990 procedure.

Analysis and prediction of mechanical characteristics of corrugated plate as primary support in tunnels

Traditional primary support made of reinforced concrete is widely applied but can bring many problems. Therefore, to study the mechanical behavior of corrugated-plate structure as primary support, several finite-element simulations in different sizes, shapes and elements were carried out. Besides, to ensure the exactness and practicability, a verification experiment and a BP neural network for prediction were done. The result shows that the outcome of beam-element and shell-element model is similar and the main deformation and stress is respectively down and compressive. And the difference between horseshoe-shaped and circular tunnel is small in aspect of vertical displacement and stress. Then, when t (thickness) increases, d (maximum vertical deformation) and s (maximum stress) decrease more and more slowly. When w (width) ascends, d and s improve more and more slowly. When h (height) becomes bigger, d declines more and more slowly and s goes down slowly, fast and slowly again. The outcome of the experiment conforms with the simulation. Next, by BP neural network, using top load and t, w, h to predict d and s is feasible and efficient. It performs better when predicting d. This paper can provide reference for the application of corrugated-steel-plate structure as new-type primary support.

A study of forming of thin-walled hemispheres by mandrel-free spinning of commercially pure aluminum tubes

Abstract The purpose of this research is to understand the effect of process parameters in multi-pass, mandrel-free, room-temperature tube-spinning, and in particular the role of axial feed-rate on the shape and thickness change when producing a hemisphere. This is tackled with a combination of experiments and analysis. The material of this study is heat-treated, commercially-pure aluminum (AA1070) tubes of 100 mm diameter. To produce the hemisphere, seven linear passes are selected. The spinning experiments are conducted for two tube thicknesses (2 mm and 3 mm) under three different axial feed-rates (2, 5, and 7.5 mm/rev.) and identical radial feed-rate (5 mm/pass). It is found that decreasing the axial feed-rate generates less spatial variation in the final thickness, while also making the process slower. During every experiment, the tube wrinkles axially. The experiments are interrupted after different spinning passes, and the shape and thickness are measured. Three different finite element models are described, using axisymmetric, shell and solid elements, respectively. Comparing them to the experiments shows that the computationally-efficient axisymmetric model gives reasonable shape and thickness predictions. The shell element model tends to overpredict the shape and thickness evolution during spinning, while being about 250 times slower. Finally, the solid element model provides good agreement with the experiments across the board, while being only 2 times slower than the shell element one. Hence it is recommended for industrial practice to use the axisymmetric model for preliminary process design (i.e., selection of toolpath and process parameters) and then to refine these selections with the solid element model.

Thermal free vibration analysis of functionally graded plates and panels with an improved finite shell element

This article deals with thermal free vibration analysis of functionally graded material (FGM) plates and panels using an improved first-order shear deformable (I-FSDT) shell model. The Effective material properties of the FGMs are estimated according to a power law distribution with temperature dependency. The FGM structure can be subjected to uniform or nonlinear temperature rise. The results obtained from the proposed formulation are validated with those available in the literature. Natural frequencies of FGM plates and cylindrical panels are computed for different power law indexes, thermal loadings, boundary conditions and aspect ratios. The present (I-FSDT) finite shell element model is much like the standard (FSDT) model but does not need shear correction factors and is of high accuracy. This work is the first application of the formulation to free vibration analysis of FG plate and shell structures including thermal effects.

A new method of predicting hotspot stresses for longitudinal attachments with reduced element sensitivities

For the complicated structural details in ships and offshore structures, the traditional hotspot stress approaches are known to be sensitive to the element variables of element topologies, sizes, and integration schemes. This motivated to develop a new approach for predicting reasonable hotspot stresses, which is less sensitive to the element variables and easy to be implemented the real marine structures. The three-point bending tests were conducted for the longitudinal attachments with the round and rectangular weld toes. The tests were reproduced in the numerical simulations using the solid and shell element models, and the simulation technique was validated by comparing the experimental stresses with the simulated ones. This paper considered three hotspot stress approaches: the ESM method based on surface stress extrapolation, the Dong's method based on nodal forces along a weld toe, and the proposed method based on nodal forces perpendicular to an imaginary vertical plane at a weld toe. In order to study the element sensitivities of each method, 16 solid element models and 8 shell element models were generated under the bending and tension loads, respectively. The element sensitivity was analyzed in terms of Stress Concentration Factors (SCFs) in viewpoints of two statistical quantities of mean and bias with respect to the reference SCFs. The average SCFs predicted by the proposed method were remarkably in good agreement with the reference SCFs based on the experiments and the ship rules. Negligibly small Coefficients of Variation (CVs) of the SCFs, which is measure of statistical bias, were drawn by the proposed method.

Considering inhomogeneous material properties for stiffness and failure prediction of thin-walled additively manufactured parts

By overcoming manufacturing constraints imposed by traditional production technologies, additive manufacturing enables engineers to realize highly optimized lightweight components of unmatched geometrical complexity. However, the common dependency of the mechanical material properties on build orientation and wall thickness constitutes a challenge for valid structural analyses of thin-walled parts. Hence within this research, a previously proposed strategy to improve the structural simulations by mapping inhomogeneous material properties into finite shell element models is extended for failure prediction. Therefore, coupons in various build orientations and thicknesses were produced of short fiber-reinforced polyamid 12 via laser sintering and the mechanical properties evaluated by means of digital image correlation-assisted tensile testing. Consequently, the obtained data is utilized for modeling of the thickness dependent and anisotropic material behavior. The inhomogeneous material parameters are automatically mapped in the finite element models and ultimately, numeric simulations are validated by experimental testing of thin-walled parts. The comparisons of finite element analyses with mapped inhomogeneous and conventional constant properties disclosed considerably improved prediction of stiffness and failure. For the latter, however, substantial deviations between simulation and physical experiment remained, indicating that further research is necessary to effectively asses the load bearing capacity of thin-walled additively manufactured structures.

FINITE ELEMENT ANALYSES ON CORRODED PONY TRUSS BRIDGE FOR REASONABLE MAINTENANCE

The load bearing capacity of an existing corroded pony truss bridge, which is used for 100 years was estimated from FEM results for whole bridge model. The beam element model is to clarify that the influence of the residual out-of-plane deformation in main truss structures on the load bearing capacity from the viewpoint of whole bridge. Also, shell element model is to clarify that the influence of severe corrosion damages occurred in many structural members on the load bearing capacity as whole bridge. On the other hand, the influence of assumed support conditions in analytical models were discussed from the analytical results of both type of models, because it will be thought that the performance of shoes deteriorates gradually by long in-service period. The ultimate load bearing capacity was estimated by the critical live load magnification. From the analytical results, the residual out-of-plane deformation of main truss structures in this bridge had little influence on the ultimate load bearing capacity. Also, the ultimate load bearing capacity may decrease up to 20% due to aging deterioration of shoes including corrosion damages. In bridge maintenance, it should be paid attention on local severe corrosion damages on the structural member, which may occur higher secondary stress.

Adaptive Powell’s Identification of Elastic Constants of Composite Glass Girder with Layered Shell Element Theory

For the composite glass box girder, the generalized Bayesian objective function of elastic constants of the structure was derived based on layered shell element theory. Mechanical performances of the composite glass box girder were solved by layered shell element method. Combined with quadratic parabolic interpolation search scheme of optimized step length, the adaptive Powell’s optimization theory was taken to complete the stochastic identification of elastic constants of composite glass box girder. Then the adaptive Powell’s identification steps of elastic constants of the structure were presented in detail and the adaptive Powell’s identification procedure was accomplished. From some classic examples, it is finally achieved that the adaptive Powell’s identification of elastic constants of composite glass box girder has perfect convergence and numerical stability, which testifies that the adaptive Powell’s identification theory of elastic constants of composite glass box girder is correct and reliable. The stochastic characteristics of systematic responses and elastic constants are well deliberated in generalized Bayesian objective function. And in iterative processes, the adaptive Powell’s identification is irrelevant with the complicated partial differentiation of the systematic responses from the layered shell element model to the elastic constants, which proves high computation efficiency.

자동격자생성 알고리듬을 이용한 주름관을 갖는 배관계의 효율적 진동 분석

In this study, an automatic mesh generation algorithm was developed for efficient finite shell element modeling of piping systems with bellows. For pre-processing of finite element analysis, a pipe geometry should be modeled using meshing software. However, the finite element meshing process requires time-consuming efforts for complicated piping systems such as bellows. Therefore, this study proposed an algorithm that can efficiently generate finite shell elements automatically. To generate the finite shell element model of the pipe, this algorithm only needs the information of the centerline of the pipe and the corresponding radius that is identical to the finite beam element. Additionally, effects of bellows on the dynamic characteristics of a curved pipe were discussed. The variation of the natural frequencies and dynamic stiffness of the piping system with respect to the change of the location, height and width of the bellows were investigated. The suggested automatic mesh algorithm is advantageous for the modeling of pipes having complex shapes such as bellows. Hence, it has the potential to be useful in designing optimal bellows in piping systems that require numerous finite element analysis calculations.

Analysis of Load Noise Components in Small Core-Form Transformers

We propose load noise analysis components for small core-form transformers (1 MVA–20 MVA) using computational fluid-structure coupled calculations that consider the electromagnetic force, transformer structure and fluid (oil). The proposed technique has two beneficial aspects: coil modeling using shell elements of the finite element method (FEM), and acoustic noise analysis using a combination of boundary element method transmission path simulation and FEM structural simulation. The shell element model, which includes structural bending information, is less computationally intensive for simulations than solid models because it uses larger element sizes. Lighter simulations enable easier redesign for noise reduction. Additionally, division of the simulation process into individual structural vibrations, transmission paths, and radiation processes makes it easier to find a remodeling point without performing a complete simulation. We illustrate the importance of avoiding coincidence of the natural frequencies of the coils and the electromagnetic force and present a practical noise reduction study. This technique can be implemented using a light simulation that was proposed to confirm the remodeling effects. Using the proposed analysis method along with a ray tracing method, we can construct a frontloading design simulation tool to determine the transformer specifications and the substation's geographical features.