Shell FE Research Articles

New beam-based models for fire-induced buckling analysis of class 4 steel columns

Steel cross-sections with thin walls are vulnerable to fire-induced buckling instability, which reduces their load-bearing capacity. Eurocode 3 design provisions have been found inadequate, leading to alternative methods such as effective design strategies and advanced structural models built mostly with shell FE, which can be complex. For Class 4 steel beam-columns subjected to fire conditions, beam-type modelling to predict the Flexural-Torsional Buckling (FTB) strength has been proposed as an alternative approach, but it has not yielded satisfactory results for large compressive load eccentricities. This paper presents two new low computational cost modelling strategies based on Timoshenko's beam FE to address this issue: the Single beam-column Model (SbcM) and the Cruciform beam-column Model (CbcM). The first consists of a single line of beam FE, while the second uses a grid of beam FE for more flexibility. Both strategies effectively simulate the FTB behaviour in Class 4 steel beam-column during a fire, offering quicker computations compared to shell models. Still, the single-line model is favoured for its simplicity, making it more efficient in analysing complex fire engineering problems.

Pure/combined buckling mode calculation of thin-walled members constraining general shell FE models

This paper proposes a technique for decomposing the buckling solution of thin-walled members into pure deformation modes (global, distortional, local, or other), aiming at providing an insight into the buckling behavior of these members. The calculation of critical loads associated with a specific or combined deformation mode is performed constraining general finite element models. A general constraining procedure is presented, in which the critical load of any mode, combining different section deformation modes and different harmonic shape functions in the longitudinal direction, can be determined. Cases where all possible harmonic terms may be automatically considered are also described. Cross-section deformation modes are defined in the context of the constrained finite strip method (base vectors), and the proposed constraining procedure is implemented by means of relationships between degrees of freedom of the finite element mesh in commercial software. Calculation of combined buckling modes inherently makes it possible to quantify the participation of the considered modes, including along specific longitudinal segments of the member. Results from the analysis of a lipped channel member are presented to demonstrate the concepts and, later, the analysis of a member with a more complex cross-section and intermediate boundary conditions along length is detailed. A discussion on the base vectors chosen for the constraining method is presented. Finally, the potential of the proposed method is discussed.

Design of Steel Columns in Fire using Second‐order Inelastic Analysis with Strain Limits

AbstractIn this paper, a structural steel fire design approach using second‐order inelastic analysis with strain limits is proposed and applied to the design of steel columns in fire. The proposed design approach employs beam finite elements to conduct a second‐order inelastic analysis. Within the proposed method, strain limits are used to account for the effects of local buckling; while global instability, the loss of strength and stiffness and thermal effects are fully considered through second‐order inelastic analysis carried out using beam finite elements. The proposed method is assessed against validated shell FE results. It is observed that the proposed design approach provides consistently accurate and safe capacity predictions for steel columns in fire.

An Elasto‐plastic Finite Element for the Analysis of Planar Steel Beams

AbstractThe following paper presents an original finite element formulation for the elasto‐plastic analysis of planar homogeneous isotropic beams. The one‐dimensional elastic‐perfectly plastic material behavior is considered. The approach is based on innovative shape functions able to capture the formation of elasto‐plastic regions at the ends of the beam element. While the proposed shape functions can theoretically handle any cross‐section, in this paper the formulation is developed only for rectangular cross‐sections. Linear geometric behavior is considered. The formulation is validated by comparisons with the upper bound method of plastic limit analysis in terms of ultimate loading, and with simulations using shell FE analyses in terms of load‐displacement response and development of the plastic regions.

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.

Buckling analysis of ring stiffened thin cylindrical shell under external pressure

Submarine pressure hulls, fire-tube boilers, vacuum tanks, oil well casings, submersibles, underground pipelines, tunnels, rocket motor casing, etc., are some of the examples of thin cylindrical shell structures which collapse due to buckling under uniform pressure. To enhance the buckling strength of bare cylindrical shells, one of the best solutions is to stiffen them with ring stiffeners. In this work in order to predict the shell instability failure mode (SIFM) and general instability failure mode (GIFM) FE models are generated and analysed using buckling analysis of general-purpose FE software ANSYS. The numerical results obtained using FE analysis are compared with published analytical and experimental results. Hence in the present study efforts are taken to develop FE models to predict global and shell instability failure modes of externally ring stiffened cylindrical shells by using linear FE analysis. It is proposed to use full/half bare cylindrical shell FE models (L/R ratio upto 200) to determine SIFM and FE models with shell281- Beam189 (for stiffeners) can be used to determine GIFM. The developed FE models are validated by comparing numerical results with experimental results published by Seleim and Roorda [25]. By using both proposed FE models it is possible to predict the failure modes namely SIFM and GIFM, comparing their values of critical buckling pressures. The lower pressure value can indicate the possible failure mode.

The influence of imperfections in the critical temperature of I-section steel members

This paper describes the influence of the imperfections in the critical temperature assessment of steel members at elevated temperatures. An extensive numerical investigation using shell FE models is performed in the scope of this work to calculate the critical temperature of steel members for particular combinations of geometric and material imperfections, such as member or plate imperfections and residual stresses, respectively. The behaviour of axial compressed members with I-shape section, both for flexural buckling in the strong- and weak-axis and the lateral-torsional buckling of beams, is analysed considering four different load-levels. The results show that the influence of imperfections increases with the load-level and that the critical temperature of steel members, as expected, decreases with the presence of imperfections. Particularly, the influence of the residual stresses is almost negligible for lower load-levels and could be disregarded in the numerical analyses, however, for a load-level of 65% of the load-bearing capacity, calculated at normal temperature, it is recommended that the residual stresses are included in numerical simulations, since their effects are non-negligible, especially for welded members.

On FEM analysis of Cosserat-type stiffened shells: static and stability linear analysis

The present research investigates the theory and numerical analysis of shells stiffened with beams in the framework based on the geometrically exact theories of shells and beams. Shell’s and beam’s kinematics are described by the Cosserat surface and the Cosserat rod, respectively, which are consistent including deformation and strain measures. A FEM approximation of the virtual work principle leads to the conforming shell and beam FE with 6 DoFs (including the drilling rotation for shells) in each node. Examples of static and stability linear analyses are included. Novel design formulas for the stability of stiffened shells are included.

Three-dimensional finite element modeling of rotary-draw bending of copper-titanium composite tube

The copper-titanium bimetallic composite bent tube, which could integrate the advantages of physical, chemical, and mechanical properties of two materials, shows an urgent application demand prospect in mechanical manufacturing, marine operations, and other industrial fields. This paper develops a research on the modeling of rotary-draw bending of copper-titanium composite tube by using two kinds of grid elements S4R and C3D8R, respectively. The contact problem of base tube and covered tube is set as coulomb friction contact mode, whose optimal friction coefficient is obtained by pressure-shearing experiment and its simulation. The springback model is established by considering the contact action of the two tubes. Finally, the S4R shell FE model is compared with the C3D8R solid FE model from the two aspects of section deformation and springback. It is found that the shell element model is accurate in predicting the springback and section deformation, while the solid element model has a large deviation from the experimental results in predicting the section deformation. In order to gain a deeper understanding of the plastic deformation behavior of the bimetallic composite tube, the tangential stress, equivalent stress, equivalent strain, and damage values have been studied. Results show that (1) there is no significant uneven deformation between the base tube and the covered tube, which will not produce obvious wrinkling and section distortion even without the filling of the mandrel dies. (2) Sliding and stratification are existing between the base tube and the covered tube in the bending process. (3) The force of the dies on the base tube is transmitted through the side surface contact between the base tube and the covered tube. (4) The maximum damage value of the covered tube is larger than that of the base tube. This research will promote the development of precise plastic processing technology and play a role in the research of secondary plastic forming of metal composite tubes.

Constrained shell finite element method for elastic buckling analysis of thin-walled members

Abstract The objective of this paper is to develop a constrained shell Finite Element Method (cFEM) based on a force approach for elastic buckling analysis of thin-walled members. The new cFEM is able to separate the general deformation of thin-walled members into the three fundamental deformation mode classes, namely Global (G), Distortional (D), and Local (L), to enable the modal decomposition and identification. In this paper, four force-based mechanical criteria are defined to separate these mode classes. These mechanical criteria are implemented with the general shell finite element formulation without any special treatment of the element formulation. The constraint matrices of the G, D, and L mode classes are then constructed. Numerical examples are presented to demonstrate the capabilities of the new cFEM in modal decomposition and identification. In particular, the modal decomposition and identification results are compared with the cFSM solutions. Applicability of the new cFEM to other shell FE formulation and different loading conditions are illustrated. All these numerical examples demonstrate the potential of the developed cFEM in taking advantages of the modeling capability of the existing shell FE method.

Norgesporten road bridge, the gateway to Norway

ABSTRACTThe Norgesporten bridge, in the town of Ørje in Norway, provides a landmark on arrival in Norway on the E18 Stockholm‐Oslo highway. The bridge was completed in 2017 for Staten vegvesen, the Norwegian Public Roads Administration (NPRA). The bridge, with two traffic lanes and a pedestrian/cycle path, carries local traffic over the E18. A 75m span cable stayed bridge with a curved steel deck and a 50m high, slender steel pylon asymmetrically located on the outer curve. There are 10 deck cables and five backstay cables connecting the pylon to a concrete counterweight foundation. All cables are ϕ60mm locked coil strand. The main architectural feature of the bridge is the slender, spindle‐shaped pylon, 1.9m maximum diameter, which is restrained in three directions by the cables that cross to create a complex shape and volume. The steel deck is a multi‐cell box girder, 2.1m deep, with cantilever ribs at 6m centres. The orthotropic top plate is stiffened longitudinally with trapezoidal sections. The bridge's complex geometry was analysed using both frame and shell FE models with SAP2000. A full 3D geometric model was used to develop the project drawings and as a basis for the Contractor's own 3D Tekla fabrication model. The bridge has been designed and fabricated in accordance with NPRA Handbooks N400, R410, and R762, with strict requirements for future inspection and maintenance and the box girder is fully accessible and includes dehumidifying plant. The pylon section is designed as inaccessible and airtight. The steel is painted with a duplex system for corrosion protection. The steel deck made up of 25 sections, and the pylon, in three parts, were fabricated in Riga, Latvia before transportation and site welding. During the fabrication process strict controls of the bridge geometry were carried out including partial trial assemblies of the completed sections.

Experimental and numerical study of geometrically nonlinear behavior of corrugated laminated composite shells using a nonlinear layer-wise shell FE formulation

This paper presents experimental and numerical studies on the geometrically nonlinear behavior of corrugated laminated composite shells (CLCS) under quasi-static loading along the corrugated direction. A geometrically nonlinear layer-wise shell finite element formulation is adopted to study the behavior of CLCS under large deformation by modeling of incremental different moduli in the tensile and compressive regimes through the thickness, where the spatial location of neutral axis shifts with deformation. A master curve is presented to estimate the value of compressive modulus from given tensile and flexural moduli. Using the prepreg autoclave method, the paper also describes practical challenges in the manufacturing of CLCS and reveals significant influence of thickness on the nonlinear elastic behavior of two thin and moderately thick CLCS. The proprietary layer-wise shell FE formulation is verified with solid-finite-element modeling and employing a developed user material (USERMAT) subroutine in the commercial software ANSYS. Resulting improvements in numerical modelling are assessed in both general and local behaviors.

Development of a Practical Straightening Simulation for Welded Structures Using Inherent Strain Method

Welding is the most widely used assembly method available to industries in the construction of metal structures, ships, and offshore platforms. However, this method always produces a certain amount of distortion that will not only degrade the performance but also increase the building cost of the structure, and it should be straightened. Murakawa [1] developed a thermal elastic plastic based and inherent strain based welding simulation FE code JWRIAN. Coarse shell FE models are usually used in the inherent strain based JWRIAN elastic analyses. This drastically reduces the manpower needed for modeling and computer resources needed for the calculation. However, it is not easy to perform straightening analysis using JWRIAN because gas heating’s inherent strain distributes over a range much smaller than element sizes of the shell model.RUIZ [2] modified JWRIAN’s code so that the inherent strain equivalent nodal forces along the heating line are calculated and applied in the elastic shell analysis. However, a discrepancy between 3-dimensional thermal-elastic-plastic analysis and elastic analysis was observed. This is mainly because of the nature of solid and shell elements. RUIZ [3] proposed a linearized inherent strain and applied it to both 3-d and 2d analysis, getting matching results between solid and shell element models. In this study, as a working example, a thin plate panel with an opening is considered utilizing the developed system at the same time a friendly user interface for staffs and workers on a production site is developed. Keywords: Inherent strain, straightening, finite element method, Gauss-Legendre quadrature

Possibilities of the Additional Damping of Unidirectional Fiber Composites by Implementation of Viscoelastic Neoprene and Rubber Layers

The aim of the presented work is to assess modal, transmission, and damping characteristics of layered carbon plates. The base is to carry experimental analysis verified by FEM model, which evaluates the vibration transfer of tested composites and describes possibilities of additional damping by implementation of viscoelastic layers. Preimpregnated carbon fibers known as prepreg were used for creation of the samples composed of four (2 constant and 2 variable) layers. The task was to assess impact of changing the fiber orientation on the transfer function and individual modal characteristics. As another option, testing of some additional damping materials was included. Neoprene and thin rubber coat were added as an outside damping element when the neoprene ply was inserted also among the layers. Expected dependence of the plies orientation onto the shape of the transfer function and even swapping of some of MOD characters (bending, torsion, and their combinations) have been found. The use of the additional damping materials is also possible but the right combination of the individual plies layout and stacking sequence is the most significant part. The results had been statistically analyzed and showed that the created layered shell FE models could be used to describe the behavior.

선체 Shell FE 모델 내 용접부의 Solid 요소변환 자동화 시스템

선체 Shell FE 모델 내 용접부의 Solid 요소변환 자동화 시스템

A Continuum Shell-beam Finite Element Modeling of Buried Pipes with 90-degree Elbow Subjected to Earthquake Excitations

In the current work, the seismic analysis of bent region in buried pipes is performed, and effects of soil properties and modeling methods on pipe ’s response are investigated. To do this task, beam, beamshell finite element modeling, and a continuum shell FE model of a 90-degree elbow are employed. In the beam model, the pipe is simulated by beam elements while combined shell-beam elements are used for the continuum shell finite element model. The surrounding soil is simulated by nonlinear springs and solid elements; moreover, soil hardening behavior and soil-pipe slippage are considered in the models. In addition, an equivalent boundary condition has been employed at the end of each elbow leg to simulate far field effects more closely. From these analyses, it can be revealed that axial strain at bends is larger in stiffer soil due to smaller slippage. In addition, a full three dimensional soil-pipe interaction using continuum shell FE model causes a substantial increase of elbow strain.

An investigation into thickness distribution in single point incremental forming using sequential limit analysis

Single point incremental forming (SPIF), needing no dedicated tools, is the simplest variant of incremental sheet metal forming processes. In the present work, a simplified model of SPIF of a truncated cone, capable of predicting the thickness distribution, has been developed using sequential limit analysis (SLA). The obtained results were validated experimentally and compared with thickness predictions obtained from an explicit shell FE model implemented in Abaqus. It is shown that SLA is capable to solve the thickness prediction problem more accurately and efficiently than the equivalent FEA approach. As an application of the proposed model, the effect of the diameter of the hemispherical tool tip and the step down on the thickness distribution and the minimum thickness in a 50° cone is studied using SLA. By introducing bending and stretching zones in the wall of the cone, variations of the minimum thickness by changing the tool diameter and the step down are discussed.

Study on the preciseness of hot spot stress of web-stiffened cruciform welded joints derived from shell finite element analyses

A new simple and accurate shell FE-based structural Hot Spot Stress (HSS) determination method for web-stiffened cruciform joints has been proposed. Local stress of welded joints in full-scale bulk carrier (BC)’s lower stool models subject to bending and pressure loadings are examined. HSSs determined by the proposed method are compared with those derived by Lotsberg’s method and the conventional 0.5 t–1.5 t extrapolation. As results, following are found: (1) The local stress of full-scale BC lower stool models with various stool angle and plate thickness can be calculated accurately solely from shell FE results by means of the proposed method. (2) HSSs of welded joints in full-scale BC lower stool models subject to bending and pressure loadings derived by the proposed method show good agreement with the target HSSs determined from fine solid models. This demonstrates the validity of the proposed method for actual ship structures under the real load. (3) The excessive safety allowance of HSS determined by the conventional 0.5 t–1.5 t extrapolation can be reduced substantially by adopting Lotsberg’s method or our proposal. The proposed HSS determination method gives more accurate estimates compared to Lotsberg’s method under the conditions chosen, and the application range of the proposed method is equal to or wider than Lotsberg’s method.

Study on the Preciseness of Hot Spot Stress of Web-Stiffened Cruciform Welded Joints Derived by Shell Finite Element Analyses

A new simple and accurate shell FE-based structural Hot Spot Stress (HSS) determination method for web-stiffened cruciform joints has been proposed. Local stress of welded joints in full-scale BC lower stool models subject to bending and pressure loadings are examined. HSSs determined by the proposed method are compared with those derived by Lotsberg's method (Lotsberg et al., 2007) and the conventional 0.5t-1.5t extrapolation. It is shown that the local stress of full-scale BC lower stool models with various stool angle and plate thickness can be calculated accurately solely from shell FE results by following the proposed method. HSSs of welded joints in BC lower stool models subject to pressure loadings derived by the proposed method show good agreement with the target HSSs. This demonstrates the validity of the proposed method for actual ship structures under the real load. The proposed HSS determination method has advantage over Lotsberg's method in the accuracy and application range.

Evaluation of Effects of Wave-induced Vibrations on Fatigue Damage of Large Ships

Low frequency response to normal wave loads and high frequency response due to wave-induced vibrations coexist in the ship's structural loads. This paper addresses the effect of the wave-induced vibrations on long-term fatigue damage in various types of ships. A bulk carrier, a VLCC, and a container carrier are employed as subject ships. A weakly nonlinear method proposed by one of the authors is employed for evaluating the load effects. Slamming loads are separately implemented by using momentum theory.The whole ship is represented by using shell FE model. The calculations are performed for various short-term sea states. Stress cycles are counted by using Rainflow counting method. Then, long-term fatigue damage is evaluated by using the Palmgren-Miner rule. A series of sensitivity analysis is also performed to clarify the characteristics of the fatigue damage by the wave-induced vibrations in oblique seas as well as in head seas. It is shown that the amount of the increase in fatigue damage depends on the wave load characteristics of the ships in waves as well as the structural properties such as natural frequencies of flexible mode.