Shell Finite Element Model Research Articles

Correlating Skeletal Muscle Output Force and Intramuscular Pressure Via a Three-Dimensional Finite Element Muscle Model.

The inclusion of muscle pressure in muscle models may have important implications in biomechanics. This notion builds from the known correlation between muscle contractile force and internal pressure. However, this relation is often omitted in numerical models leveraged to study biomechanics. Thus, the purpose of this study was to develop and validate a method of modeling muscles, via finite elements, inclusive of the correlation between muscle contractile force and intramuscular pressure. A magnetic resonance imaging (MRI)-scanned tibialis anterior muscle was modeled via a simple, yet easily scalable, mixed shell and pressure finite element model. Then a validation study was conducted on intramuscular pressure, resulting from applied muscle contractile force, through leveraging special fluid elements type. The fluid-structure-based model and adopted methods exhibited muscle forces and intramuscular pressure that were highly linearly correlated. Indirect validation was achieved with a maximum discrepancy of 7.25%. Furthermore, force-length curves followed a trend similar to documented conventional muscle data, which added to the model's validity. Mesh, material properties, and tendon stiffness sensitivity studies supported the model's robustness. This study has introduced a novel three-dimensional finite element modeling method that respects the physiological force and intramuscular pressure relationship. Although similar models have been previously explored, their complex physiological representation and time-consuming solvers make their scalability and real-time implementation questionable. Thus, the developed model may address such limitations while improving the realism of volumetric finite element models inclusive of muscle contribution.

Testing, simulation and design of steel equal-leg angle section beams

The stability and design of steel equal-leg angle section members subjected to uniaxial bending are studied herein. An experimental investigation, comprising material testing, initial geometric imperfection measurements and physical tests on hot-rolled steel equal-leg angle section beams is first presented. The test results, in combination with existing experimental data on steel equal-leg angle section beams collected from the literature, are then used for the validation of numerical (shell finite element) models, developed within the commercial package ABAQUS. Next, a numerical parametric study is presented considering both hot-rolled and cold-formed steel angle section beams with a wide range of slenderness values. In major-axis bending, both lateral-torsional and local buckling were observed, with the former characterised by lateral deflection and twist of the cross-section along the member length but no cross-section deformation and the latter by relative twist and transverse bending of the outstands. In minor-axis bending, lateral-torsional buckling and Brazier flattening were observed, with the latter characterised by splaying of the outstands. Note that, for equal-leg angles under minor-axis bending, lateral-torsional buckling is dominant when the cross-section tips are in compression, while Brazier flattening is more influential when the cross-section tips are in tension. When designing for major-axis bending according to Eurocode 3, both local and lateral-torsional buckling are considered; it is shown herein that equal-leg angle section beams under major-axis bending can be designed using a normalised slenderness based on the minimum of the local and lateral-torsional elastic buckling moments, while also considering the ratio of the local to the lateral-torsional elastic buckling moments. For minor-axis bending, Eurocode 3 only requires cross-section checks; this is found to result in unsafe predictions in some cases. It is shown that both safer and more accurate resistance predictions can be achieved when lateral-torsional buckling and Brazier flattening are accounted for in the design of equal-leg angle section beams under minor-axis bending, using a normalised slenderness, based on the minimum of the lateral-torsional and Brazier flattening critical buckling moments. Finally, new design proposals for steel equal-leg angle section beams, covering both major- and minor-axis bending, are developed and verified against the experimental and numerical results. The proposed design rules are shown to offer substantially more accurate and consistent resistance predictions compared to existing codified design rules. The reliability of the new design provisions, with a recommended partial safety factor γM1=1.0, is verified following the EN 1990 procedure.

Improved structural design of wind turbine blade based on topology and size optimization

Abstract In order to compete with traditional power technologies and other energy sources, it is essential to use optimization techniques as part of the design process for wind turbine blades. This paper presents an optimization approach for the improved structural design of blades, aiming at further decreasing the blade mass and bringing down the cost. The optimization approach mainly consists of two steps. In the first step, topology optimization of a full 1.5 MW wind turbine blade is carried out with the expectation of finding an improved internal structural configuration by taking minimum compliance as an objective. In the second step, the topology optimization results are interpreted to create a shell finite element model of the blade to analyse the influence of distinguishing characteristic parameters on the blade performances; then, size optimizations of the blades with improved structural configuration and conventional structure are performed by considering the minimum mass as objective, key structural parameters as variables, strain, deflection, vibration and buckling limits as constraints. The final optimization results show that the blade with improved structural configuration can reach a further mass saving of 3% compared with the optimized conventional structure design, indicating that the proposed approach is effective and reliable.

A Comparison of Shell and Solid Finite Element Models of Austenitic Stainless Steel Columns in Compression

The subject of this article is the implementation of new knowledge on material and geometric characteristics obtained from an experimental research program in advanced numerical modelling of compressed columns made of austenitic stainless steel using the ANSYS Classic software. Nonlinear stress–strain curves were obtained using our own experimental program and studied in terms of identifying the most suitable nonlinear material model. Additional material and geometric characteristics were obtained from literature and other independent research. Numerical models differing in mesh density localization, formulation of element integration, non-linear material model, and initial geometric imperfections were created and compared. The aim of the models was the ultimate limit state of a strut of circular hollow cross-section stressed by compression and analysed using the geometrically and materially nonlinear solution with consideration to the influence of initial imperfections. Static resistance and limit state deformations are compared for each model. The paper presents the analysis of model uncertainty by comparing SHELL and SOLID FE models, which must be characterized before the start of the analysis of the random influence of imperfections on the limit states. The mean values and the coefficients of variation are practically the same for both approaches. In summary, the presented models can be considered sufficiently validated and eligible for integration in tandem with simulation sampling methods.

Numerical investigation into thermal buckling of friction pairs in hydro-viscous drive under nonlinear radial temperature distribution

Thermal buckling deformation can significantly impact the operating performance of hydro-viscous drive. A thermal buckling finite element shell model was established with the nonlinear radial temperature as the thermal loading condition. The thermal buckling behavior of friction pairs was investigated under three different boundary constraints. Moreover, the influence of thickness and material parameters on the critical buckling temperature was discussed. The simulation results coincide with the failure modes of friction pairs in practice, and the most common ones are the coning mode and the potato chip mode. The ability to resist thermal buckling deformation can be improved as the thickness increases. In addition, the steel disc with outer edge simply supported is more prone to thermal buckling, because the critical temperature is minimum. The thermal expansion coefficient is the primary factor in thermal buckling study, which is inversely proportional to the critical temperature. These provide a theoretical basis for avoiding thermal failure of friction pairs in a hydro-viscous drive.

Stability and design of fixed-ended stainless steel equal-leg angle section compression members

The stability and design of fixed-ended stainless steel equal-leg angle section members subjected to axial compression are studied herein. An experimental investigation, comprising material testing, initial geometric imperfection measurements and tests on hot-rolled austenitic stainless steel equal-leg angle section columns is first presented. The test results, in combination with existing experimental data on stainless 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 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 minor-axis 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. The reliability of the new design provisions, with a recommended partial safety factor γM1=1.1, is verified following the EN 1990 procedure.

Out-of-plane stability design of steel beams by second-order inelastic analysis with strain limits

An accurate and consistent approach to the out-of-plane stability design of steel beams and structures utilising second-order inelastic analysis with strain limits is proposed. The method is implemented using computationally efficient beam elements, with the ultimate structural resistance defined either by (i) the ultimate load factor or (ii) the load factor at which a strain limit, determined on the basis of the continuous strength method (CSM), is attained, whichever occurs first. Thus far, the method has been established for the in-plane design of steel structures and structural components; in the present paper, its scope is extended, for the first time to the scenarios in which out-of-plane stability effects, with a focus on lateral–torsional buckling (LTB), govern. The accuracy and safety of the method are assessed against the results of nonlinear shell finite element (FE) modelling. It is shown that the proposed method consistently provides more accurate results than the traditional LTB design method of prEN 1993-1-1. In addition to its accuracy, the proposed approach also streamlines the design process by eliminating the need for cross-section classification and member design checks.

Numerical Simulation and Design of Stainless Steel Columns under Elevated Temperatures

AbstractThis paper presents and discusses the first results of an ongoing Abaqus numerical (shell finite element) investigation on stainless steel columns under elevated temperatures and prone to local or global buckling, performed in the context of the project “StaSteFi ‐ Fire Design of Stainless Steel Members”. In particular, geometrically and materially non‐linear shell finite element models are employed to obtain the failure loads of columns (i) with several cross‐section shapes (SHS, RHS, CHS, EHS and I‐section), (ii) prone to local or global buckling, (iii) made from three stainless steel grades (ferritic 1.4003, austenitic 1.4301 and duplex 1.4462), (iv) subjected to various elevated temperatures (θ=100, 200, 300, 400, 500, 600, 700 and 800°C) and (v) containing both initial geometrical imperfections and residual stresses. The failure loads gathered are then used to assess the prediction quality of the Eurocode 3 stainless steel design rules and explore the development and calibration of novel design approaches.

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.

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.

Combining shell and GBT-based finite elements: Vibration and dynamic analysis

This paper extends the approach previously proposed by the authors Manta et al. (2020, 2021) to the dynamic case, more precisely to the calculation of natural frequencies (including pre-loaded members) and the linear time-history response of thin-walled members and frames with complex geometry, undergoing global–local–distortional deformation. This approach relies on a combination of standard shell and GBT-based (beam) finite elements, where the prismatic beam parts are modelled with standard GBT-based elements with a minimum number of deformation modes (hence a minimum number of DOFs), while the geometrically complex zones (perforations, tapering, joints) are handled using shell elements. Three numerical examples are presented to demonstrate the capabilities and potential of the proposed approach. These examples concern (i) a lipped channel cantilever with two long holes, (ii) a lipped channel cantilever with a tapered segment, subjected to pre-loading, and (iii) an L-shaped frame with I-section members and a tapered joint. For comparison and validation purposes, full shell finite element model solutions are provided. In all examples, it is concluded that the proposed approach leads to very accurate results and a significant DOF economy with respect to full shell finite element models.

Progressive-models method for evaluating interactive stability of steel box girders for bridges – Extension of progressive collapse method in ship structures

The progressive collapse method (PCM) in ship structures, in which local buckling is simplified by average compressive stress-strain curves of stiffened plates, is extended to analyze the ultimate bearing capacity of steel box girders for bridges. The PCM for steel bridges is reconstructed as the progressive-models method (PMM). Subsequently, a detailed PMM used for large-scale steel box girders is proposed and implemented through a two-stage analysis, which includes the nonlinear analysis of stiffened plate using shell finite element (FE) model and the nonlinear analysis of member using beam-column theory. The PMM is demonstrated by using an example tested steel box girder of which the ultimate bearing capacity is influenced by local buckling. The traditional finite element (FE) models of the tested steel box girder, including the refined shell FE model, beam-column FE model and multi-scale FE model, are established to make a comparison and validate the proposed method. The results show that the stability of each stiffened plate in the studied steel box girder is different, among them the mid web, of which the ultimate strength is 0.65 times of the yield strength at the severe defect level, is the most susceptible to buckling. Compared with results of the test and traditional FE models, the PMM is conservative for predicting the ultimate bearing capacity. In addition, the comparison of the scale of models shows that the PMM proposed can significantly reduce the complexity of modeling and improve the computational efficiency, thus the PMM has potential practical application value. The PMM can be regarded as a new attempt for the ultimate bearing capacity analysis of large-scale steel bridge members.

Local stability of normal and high strength steel plates at elevated temperatures

This paper presents an investigation into the local buckling behaviour and design of normal and high strength steel plates at elevated temperatures. The considered high strength steel grades include grades S690 and S460 as well as the normal strength grades S355, S275 and S235 taken into consideration. Shell finite element models of normal and high strength steel plates are created to mimic their local buckling response in fire, whose accuracy is validated against experimental results from the literature. Extensive numerical parametric studies are then carried out by means of the validated finite element models, taking into account different plate slendernesses, elevated temperature levels, edge boundary conditions and steel grades. The accuracy of the design provisions provided in the current European structural steel fire design standard EN 1993–1-2 and its upcoming version prEN 1993–1-2 for the consideration of the local buckling behaviour of normal and high strength steel plates in fire is investigated. It is observed that the existing design rules given in both EN 1993–1-2 and prEN 1993–1-2 lead to rather scattered estimations of the local buckling strengths of high strength steel plates at elevated temperatures. New cross-section classification rules and effective width design equations for the ultimate strength predictions of normal and high strength steel plates in fire are developed. High accuracy and reliability of the proposed design rules are demonstrated.

A modified higher order zigzag theory for response analysis of doubly curved cross-ply laminated composite shells

The present theory deals with static and free vibration analyses based on higher order zigzag theory for laminated composite shells. The finite element shell model is developed considering the thickness coordinate to radius ratio (z/R) using nine noded isoparametric quadratic element. The proposed formulation satisfies the interlaminar stress continuity at the interface of laminae and zero shear boundary conditions at free surfaces. The response results obtained by the proposed formulations are compared with the published results. Moreover, new responses results of hyperbolic paraboloidal laminated shells are obtained using the present laminated shell theory and illustrated in the present study.

Natural frequency analysis of shells of revolution based on hybrid dual-mixed [formula omitted]-finite element formulation

A newly-developed, dimensionally reduced, hp-type axisymmetric shell finite element model is extended to linear elastodynamic problems of thin shells of revolution. The hp-shell finite element relies on the hybridized version of a three-field dual-mixed variational formulation, the application of which dictates the obligate usage of the inverse three-dimensional constitutive relation for homogeneous and isotropic materials, thereby ensuring the volumetric locking-free characteristic of the shell model at theory level. The fundamental fields are the a priori non-symmetric stress tensor, the displacement vector, the infinitesimal rotation vector and the hybrid variable defined on the element interfaces. Since the dimensional reduction process guided by this hybrid-mixed formulation does not necessitate the use of any classical kinematic assumptions appearing in the scientific literature, the inverse 3D Hooke’s law does not have to be modified. The numerical performance of the shell finite element is analyzed comprehensively for natural frequency computations of clamped-free and simply supported, silicone, conoid, spherical and hyperboloid shells of revolution. From their relative error convergence behaviors it follows that the extended hybrid-mixed shell finite element is not sensitive to the decrease of the slenderness ratio, namely providing reliable, uniformly stable numerical results for both h- and p-approximation. From theoretical point of view, the beneficial properties of the hybrid-mixed hp shell finite element model are as follows: (i) this is effectively applicable to modeling not only extremely thin but also moderately thick shell structures with transverse shear deformations, as well as (ii) both the through-the-thickness variation and the membrane stress normal to the shell mid-surface are retained as independent variables, making it much easier to upbuild shell model for contact problems. From numerical point of view, the nice feature of the hybrid-mixed hp shell finite element is that the global flexibility matrix of the system can be inverted block-wise at element level at cheap computational cost during the assembling procedure because of the hybridization technique.

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.

Mixed Eulerian–Lagrangian shell model for lateral run-off in a steel belt drive and its experimental validation

A non-material shell finite element model is developed and applied to the example problem of a slack steel belt moving on two rotating drums. For the first time in the open literature we demonstrate an approach for predicting the time evolution of the lateral run-off velocity of the belt in response to its geometric imperfection and angular drum misalignment. We adopt a novel Eulerian–Lagrangian kinematic description featuring a mixed parametrisation of the configurational space with a Eulerian circumferential coordinate and two Lagrangian coordinates for the transverse and lateral deflections. A nonlinear finite element approximation provides the necessary C1 inter-element continuity in this compound coordinate system. Using the model of elastic tangential contact, we account for the convective term in the local increments of the relative displacement between the contacting surfaces during the time integration. A thorough convergence study with respect to the mesh and time step sizes justifies the approach. Together with the successful validation against the results of a series of physical experiments, this makes the present contribution an important step towards a model-based controller design.

Isogeometric dynamic analysis of shells based on the nonlinear micropolar theory

Studying the large-amplitude forced vibration characteristics of micropolar shell-type structures is the main objective of this paper. In order to obtain the full geometrically nonlinear model of micropolar theory, the micromorphic seven-parameter shell kinematic is first developed. Via a nonlinear micro-motion map, the extracted formulation is fitted for the micropolar continuum. As a result, possessing three stress–strain fields with eighteen independent elastic parameters of a linear material, the proposed micropolar shell theory is able to capture the inhomogeneity and size-effects. On the basis of Hamilton’s principle, the variational form of governing equations of motion is determined. The finite element isogeometric solution approach is then utilized to produce the geometry and approximate the displacement field in mid-surface area of shell. This would be helpful for resolving the locking and instability issues of the traditional low-order standard finite element shell models. By discretizing the period of harmonic vibration, a numerical method is also implemented in time domain. To demonstrate the microstructural effects, dynamic behavior of micropolar plate- and shell-type structures are investigated in several parametric studies. Since the classical strain and stress tensors are retained in present micropolar elasticity, both the large macro- and micro-deformations are captured for the first time.

A novel modeling approach for multi-passes butt-welded plates

Numerical simulation of welding process in the industrial field requires flexibility, speed, and accuracy at the same time. The use of conventional 3D models in detailed simulations of multi-pass welds is time-consuming, and it often slows down the design phase of large welded structures. Shell elements are usually employed in the finite element (FE) simulation of large structures like vessels and pipes. Nevertheless, employing a simple shell model to simulate multi-pass welds would most likely produce inaccurate outcomes. This article introduces a new equivalent parametric modeling methodology for the simulation of longitudinal multi-pass welds on plane structures, such as plates and rectangular hollow sections. The proposed Weld Equivalent Model (WEM) is made with single and multi-layer shell, link and beam elements. It helps detect residual stress and local distortion that are typical of multi-pass welds. This method employs thermal transient and steady-state structural analyses. The WEM model is generated by an automatic subroutine acting on a pre-existing FE shell model. In addition to this, a case study is reported of multi-pass welding of two plates featuring a V-shaped groove. This innovative weld modeling technique shows remarkable results and helps shorten computational time up to ten times compared to classical 3D numerical models.

A geometrically exact beam finite element for curved thin-walled bars with deformable cross-section

This paper presents a geometrically exact beam finite element for curved and twisted thin-walled bars undergoing large displacements and finite rotations, combined with cross-section in-plane and out-of-plane (warping) deformation. The underlying formulation is based on a previous work by the authors Gonçalves et al. (2010), which is now improved and extended for the pre-curved/twisted case. Cross-section deformation is allowed for by adding kinematic DOFs, the so-called “cross-section deformation modes”, which are obtained using Generalised Beam Theory. All expressions required to implement the proposed finite element are derived. For validation purposes, several numerical examples are presented and discussed. In each case, the results obtained with the proposed element and refined shell finite element models are compared, and an excellent agreement is found. In particular, it is demonstrated that the proposed element predicts very accurately the spatial behaviour of curved beams undergoing complex coupling between large displacements, finite rotations and cross-section deformation.