Shell Elements Research Articles

An Implicit Fillet‐Weld Element Formulation for Mesh‐Insensitive Fatigue Evaluation of Complex Structures

ABSTRACTIn fatigue evaluation of welded structures, explicit weld representations in finite element (FE) models are needed for reliably capturing stress or strain concentration behaviors at critical weld locations, for example, weld toe or weld root, in using widely accepted traction structural stress or extrapolation hot‐spot stress methods. The laborious efforts needed for generating weld geometry have been a major challenge for fatigue evaluation of complex structures containing many welds. In this paper, we present a user‐defined fillet‐weld element formulation and its numerical implementation for computing traction mesh‐insensitive structural stresses. The fillet‐weld element is formulated by connecting several linear four‐nodes Mindlin shell elements around weld region as a user‐defined element. The resulting elements can be directly used with major commercial FE codes through an available user subroutine interface. A number of well‐documented fillet‐welded components are then used for validating the accuracy and robustness of the developed fillet‐weld elements.

Modeling inelastic behavior of U-shaped walls using multi-layer shell element: assessment at both global and local levels

AbstractOver recent decades, various numerical approaches have been developed to simulate the nonlinear behavior of reinforced concrete (RC) walls, with the multi-layer shell element method being commonly employed for thin RC wall structures. Although the global force–displacement relationship is often used to validate numerical models, their accuracy at the local level is seldom assessed. A recent experimental program has provided a detailed benchmark for investigating the nonlinear behavior of RC U-shaped walls under both flexure- and torsion-dominated loading conditions. This study developed a detailed finite element model to evaluate the multi-layer shell element method’s effectiveness in simulating both the global and local responses of RC U-shaped walls. At the global level, the model accurately captured the wall pre-failure cyclic hysteresis, cracking pattern and stiffness degradation. At the local level, the model’s accuracy was assessed by comparing the concrete deformation, rebar strain distribution and crack width. The results indicated that the model reasonably represented the local behavior of the U-shaped walls at small drift levels. However, the error increased with higher drift level, particularly in reproducing the concrete deformation and reinforcement strain at the wall base. This study provides insights into the capabilities and limitations of the proposed model, informing future improvements in the numerical simulation of RC wall structures.

The Behaviour of Elbow Elements at Pure Bending Applications Compared to Beam and Shell Element models

Abstract This paper studies the response of ELBOW31 and ELBOW31B element types under pure bending conditions, using shell and beam element models for benchmarking. Various model lengths are evaluated, showing that a model length of six pipe diameters exhibits a hardening effect when total strain exceeds 3.5%, though a strain up to 1% is deemed sufficient for pipeline design. The study examines the effects of ovality modes and boundary conditions such as NOWARP and NOOVAL on the bending response. ELBOW31 with one or two ovality modes yields accurate results, while additional ovality modes or zero ovality mode can lead to overprediction of the elastic bending moment capacity. The introduction of the NOWARP condition enhances the accuracy of the ELBOW31 model, while the NOOVAL condition alone produces unrealistic results. The simplified ELBOW31B model shows good agreement with the ELBOW31-NOWARP model but similarly overpredicts when zero ovality mode is used. The study also finds that Poisson?s ratio and model length have no significant impact on the bending response when no restrictions are applied. Additional analyses, as presented in Appendices A and B, highlight the importance of D/t ratios in pipeline performance. A D/t ratio of 20 offers a stiffer response with reduced ovalization, while a D/t ratio of 50 results in greater flexibility and increased ovalization. These findings provide valuable insights for the selection of element types, boundary conditions, and D/t ratios in robust pipeline design.

ANALYSIS OF REINFORCED BOLTED JOINTS IN HIGH-CAPACITY SILOS

ABSTRACT: This paper presents an analysis of the mechanical performance of bolted joints used in silos for storing bulk materials. In particular, we investigated the effectiveness of three types of bolted joints: one without reinforcement, one with angular reinforcement, and one with squared reinforcement. Our analysis involved the use of the finite element analysis sub-modeling technique, which allowed us to construct a large finite element model with shell elements and a sub-model with solid elements. By analyzing the stress state of each joint, we were able to determine the contact state and contact pressure of the bolted joint. Our findings showed that bolted joints reinforced with triangular and square plates were effective in maintaining contact pressure, even under high-pressure conditions. This study provides valuable insights into the design of bolted joints used in silos, which can help ensure their reliable and safe operation. Keywords: bolted joints, high-capacity silo, FEA sub-modeling.

Weak form quadrature shell elements based on absolute nodal coordinate formulation

Weak form quadrature elements for moderately thick shells with arbitrary initial configurations are developed under the framework of continuum mechanics and the absolute nodal coordinate formulation (ANCF). Locking problems of shell analysis are discussed. Nonlinear analysis of various shell structures is conducted. The joint constraint equations for shells with discontinuous slopes are established. Five examples encompassing static and dynamic shell analysis, post-buckling analysis of shells, as well as analysis of shells with discontinuous mid-surface slopes are examined to assess the performance of the proposed elements. Satisfactory results are obtained, validating the efficacy of the proposed elements.

Simulation and experimental analysis of traveling wave resonance of flexible spiral bevel gear system

Considering the traveling wave resonance (TWR) phenomenon of the spiral bevel gear system in the aero engine accessory casing, the flexible spiral bevel gear model is established by three-dimensional (3D) shell element and beam element. The dynamic model of flexible bevel gear system considering the change of meshing teeth pairs in the operating process is established by component mode synthesis (CMS) method and rotational modal projection method. The proposed model is verified by finite element (FE) solid model and experiment test results. On this basis, the TWR phenomenon of the bevel gear system is studied in combination with dynamic response and vibration stress experimental test. The results show that the bevel gear system has 3 nodal diameter resonance speeds within the actual operating speed range, which are one 1st nodal diameter resonance of pinion and two 1st nodal diameter resonance of gear. When the bevel gear system operates at TWR state, the amplitude corresponding to fm ± m·fr (fm is meshing frequency, m is nodal diameter number, fr is shaft rotational frequency) is larger than that corresponding to fm in the Fast Fourier transform (FFT) spectrum of the of the gear foundation vibration stress, and the vibration stress cloud map of the gear foundation shows the corresponding nodal diameter vibration shape. The research results provide a theoretical basis for feature recognition and influence law evaluation of TWR of bevel gear system.

Research on the energy absorption performance of lattice filling structures based on homogenization analysis technique

The lattice structure has great application prospects in the field of energy absorption, but the high cost of numerical analysis makes it difficult to carry out related structural designs. Therefore, this article studies the feasibility of the homogenization analysis technique for the analysis of energy absorption processes in lattice-filled structures. In the study, compression experiments and numerical simulations were conducted for four different types of unit cells (including periodic truss-lattice cells and triply periodic minimal surface (TPMS cells). In the experiments, two compression samples with different numbers of periods were designed for the same unit cell structure. The research shows that the homogenized numerical model takes a lot less time to run than the classical beam and shell element models. The results of the simulation are also in line with the data from the experiments. On the other hand, the material curve constructed based on a small number of unit cell samples has excellent analytical accuracy. This means that relevant research can obtain the material experimental data required for homogenized analysis using lattice samples with low manufacturing costs. Understanding these phenomena can provide a basis for the design of energy absorption structures.

Dynamic Analysis Techniques for Road Bridges Under Large Traffic Flows

This work focuses on the dynamic analysis of road bridges under large microsimulated traffic flows, contributing an efficient dynamic analysis framework for future fatigue, comfort or driving safety studies in which realistic interactions between vehicles are considered. Different strategies to define the loading vector in the governing dynamic equations are presented for bridges discretized with beam and shell elements. The proposed interpolation techniques for beam-like models include a recursive binary search and a novel vectorized strategy based on shape functions expanded to the entire length of the deck. These are applied to a short simply supported bridge and a very long cable-stayed bridge under traffic flows generated with a cellular automata microsimulation model. The strategies presented here reduce the computational time required in conventional load interpolation algorithms, particularly in long bridges subject to dense traffic flows. Finally, the binary search algorithm is applied to the study of bridge decks discretized with shell elements under microsimulated traffic, demonstrating that high vehicle densities increase the contribution of the transverse vibration of the slab and the potential discomfort of pedestrians.

Analysis of the cylindrical shell model using a new four node quadrilateral element compared to ABAQUS elements

Shell models and loadings are very complicated in practice, especially in civil and mechanical engineering, due to their lightweight properties and ability to resist loads. Then; numerical tests are very important for this type of structure. In this work, numerical investigations of a cylindrical shell under concentrated loads are presented. Two finite elements used for this study, the new element ACM-Q4SBE1 and the S4R element of the code “ABAQUS”. The results obtained by the two elements, ACM-Q4SBE1 and S4R ABAQUS, are in agreement. The superiority and efficiency of the flat shell element approach for thin shell structures has been confirmed.

Numerical and experimental investigation on angle multiple slit bolted connections for precast wall panels

Flat Multiple Slit Devices (MSDs) have been introduced in steel constructions located in earthquake-prone areas as compact hysteretic dampers connected to braces, and were further proposed to be employed also in other structural typologies, including aligned precast concrete walls. Nevertheless, similar angle connections needed for horizontal joints of orthogonal walls are not tackled in literature. The shape of MSDs, obtained by selective weakening by removing part of the steel area of flat plates, may allow to attain a highly ductile and stable dissipative behaviour, given local plate buckling is avoided, protecting the bolted joints through capacity design. Laser cutting as an alternative to mechanical milling introduces the possibility to easily optimise the shape of the slits in order to attain better performance under laterally imposed cyclic load. This paper analyses the application of right-angle-bent MSDs for the horizontal connection between orthogonal precast walls typical of panel structures with rigid diaphragms. In particular, bolted angle plates with hourglass-shaped multiple slits obtained after laser cutting are investigated numerically via non-linear finite shell elements and experimentally with original cyclic tests. The effect of the aspect ratio of the plate and of the restraint condition, possibly affecting the performance under imposed shear deformation due to the presence of the bent corner, is investigated by parametric analysis. Finally, general design rules and recommendations are presented.

A study on solid-shell finite element formulations applied to nonlinear thermoelastic analysis of thin-walled structures

The solid-shell elements have shown great advantages in three-dimensional (3D) finite element (FE) simulation of thin-walled structures. To overcome the numerical lockings for 3D element with a large span-thickness ratio, the assumed natural strain (ANS) method combined by either the hybrid stress (HS) or enhanced assumed strain (EAS) formulations are commonly used. In this work, two types of finite element formulations of the solid-shell elements are developed for nonlinear thermoelastic analysis of thin-walled structures, which are termed as the “ANS+HS” and “ANS+EAS” formulations. Accordingly, two eight-node solid-shell elements (CSSH8 and CSSE8) are developed based on the “ANS+HS” and “ANS+EAS” formulations, respectively. The Green–Lagrange displacement–strain relation is applied to involve the geometrical nonlinearities, and both the thermal expansion and temperature-dependent material properties are considered. Nonlinear thermoelastic equilibrium equations are constructed in the framework of the two types of finite element formulations using the Hellinger–Reissner and conventional variational principles, respectively. The proposed method can easily realize three different coupling analyses for thermal–mechanical loads by modifying the parameters of nonlinear thermoelastic equilibrium equations. Numerical examples demonstrate that the proposed method using CSSH8 and CSSE8 elements traces the nonlinear thermoelastic response of the isogrid stiffened panel as accurately as the shell, solid-shell, and solid elements of ABAQUS. Furthermore, the path-following capability of the proposed method using the CSSH8 with “ANS+HS” formulation is slightly superior to that using the CSSE8 with “ANS+EAS” formulation, but both better than ABAQUS.

Evaluating the Seismic Resilience of Above-Ground Liquid Storage Tanks

Historical seismic events have repeatedly highlighted the susceptibility of above-ground liquid storage steel tanks, underscoring the critical need for their proper design to minimize potential damage due to seismic forces. A significant failure mechanism in these structures, which play essential roles in the extraction and distribution of various raw or refined materials—many of which are flammable or environmentally hazardous—is the dynamic buckling of the tank walls. This study introduces a numerical framework designed to assess the earthquake-induced hydrodynamic pressures exerted on the walls of cylindrical steel tanks. These pressures result from the inertial forces generated during seismic activity. The computational framework incorporates material and geometric nonlinearities and models the tanks using four-node shell elements with two-point integration, specifically Belytschko shell elements. The Arbitrary Lagrangian–Eulerian (ALE) method is employed to accommodate substantial structural and fluid deformations, enabling a full simulation of fluid–structure interaction through highly nonlinear algorithms. Experimental test data are utilized to validate the proposed modeling approach, particularly in replicating sloshing phenomena and identifying stress concentrations that may lead to wall buckling. The study further presents results from a parametric analysis that varies the height-to-radius and radius-to-thickness ratios of a typical anchored flat-bottomed tank, examining the seismic performance of this common storage system. These results provide insights into the relationship between tank properties and mechanical behavior under dynamic loading conditions.

FEM simulation of vibrations in building: from volume to shell elements

The problem of vibrations in buildings situated in the proximity of railway tracks is a major concern for the resident's comfort. More and more studies focus on this problem using FEM models, with shell elements for the building's walls and floors. However, the validity of this simplification is never fully justified, and it raises questions concerning the dimensions to apply to the model. The model of a building made of 3D elastic elements is compared to its simplified version made of shell elements. Three geometries with different dimensions are tested to find the one closer to the reference model. Different shell offsets are also tested. The results show great differences of floor vibration levels, mostly for high frequencies, depending on the dimensions of the geometry and the offset. The shell configuration with the closest results to the reference model is discussed.

Seismic behavior of composite shear walls with post-casting UHPC boundary elements and CRB600H steel bars

This study investigates the seismic behavior of composite shear walls reinforced with post-casting Ultra-High Performance Concrete (UHPC) boundary elements and Colded-Rolled Ribbed Bars (CRB600H). The research aims to explore the synergistic effects of UHPC and CRB600H bars on seismic performance. Six shear wall specimens with a shear span ratio of 1.56 were subjected to cyclic loading to evaluate their failure modes, crack patterns, hysteresis behavior, stiffness degradation, ductility, residual deformation, and energy dissipation capacity. The results demonstrated that the use of CRB600H bars in boundary elements of normal concrete specimens improved post-yield stiffness and reduced residual deformation. Conversely, incorporating UHPC in boundary elements enhanced load-bearing capacity and crack control but slightly reduced ductility due to the weaker interfacial connection between UHPC and the foundation. Additionally, CRB600H bars in the web region improved load-bearing capacity while maintaining ductility comparable to HRB400 bars. The findings suggest that substituting CRB600H for HRB400 in shear-dominant regions can enhance the seismic performance of shear walls. Finally, the multi-layer shell element numerical model validated by the experimental results was encouraged to conduct parametric analysis in the future. This research supports the development of more resilient building structures by integrating high-performance materials in key structural components.

Geochemical fractionation of trace elements in ostreid and gastropod shells: A potential proxy for heavy metal pollution in Ghana’s coastal environment

The content of trace elements from Crassostrea tulipa (Ostreidae, Bivalvia) from four localities (Pra Estuary, Densu Estuary, Kpone Beach, and Anyanui Creek) along the coast of Ghana has been used as a bioindicator of environmental pollution. The lowest values of heavy metals correspond to the Crassostrea shells from Densu Estuary and Anyanui Creek, whereas the highest contents are recorded in the shells from Pra Estuary and Kpone Beach. Densu Estuary and Anyanui Creek are located in areas not affected by major industries, and only Densu is located in a densely urbanized setting. Crassostrea shells from Densu Estuary are only enriched in Ni. However, the Total Organic Carbon content of the sediments of the Densu Estuary indicates anthropogenic organic pollution not evidenced by the composition of Crassostrea shells. The Crassostrea shells from the Pra Estuary show enrichment in most of the analysed trace elements (Li, Be, V, Cu, Cr, Zn, Ga, Y, Sn, Pb, U, Th, ∑REE, and As) compared with other studied sites. This enrichment is related to heavy metals influx to the Pra River by the mining activities, extensive forest clearance, and loss of soil minerals. The Crassostrea shells from Kpone Beach present comparatively high content of some trace elements (Be, Ba, Cu, Zn, Nb, Pb, and REE). The metal pollutants are related to the input of the Heavy Industrial Area of Tema (located around 3.5 km west of Kpone Beach) and urban effluences from the Greater Accra Region. The high content of Ba, Cu, Zn, and Pb in Crassostrea is directly related to high phytoplankton productivity (mainly for diatoms) linked to the input of trace metals transferred into the marine food webs. In addition, some analyses of gastropod shells from Kpone Beach indicate that Cerithium and Nerita are more sensitive to accumulating Ni and As than Crassostrea. The values of trace metals from the Crassostrea shells of the Densu Estuary and Anyanui Creek are comparatively low. Considering the role of Crassostrea shells as bioindicators for heavy metals pollution, the less polluted localities are Anyanui Creek and Densu Estuary, whereas Pra Estuary and Kpone Beach are affected by anthropic activities such as mining, urban effluents, and industry.

Thermo-flexible coupled dynamics of composite laminated plates based on absolute nodal coordinate formulation

In this paper, a thermo-flexible coupled dynamic model of composite laminates is established by Absolute Nodal Coordinate Formulation (ANCF). In order to solve the problem of mesh mismatch and precision inconsistency between the displacement and temperature fields in the traditional thermo-flexible coupled modeling method, the ANCF hybrid element with integrated temperature description is constructed to achieve a unified description of the displacement and temperature fields. A new ANCF thin shell element with thermal effects is proposed. Based on the first law of thermodynamics, the heat capacity matrix, thermal conduction matrix, blackbody radiation matrix, internal heat source vector, and heat flux density vector caused by solar radiation for the ANCF thin shell element considering thermal effects are derived. The dynamic equation of ANCF composite laminates under a unified description is derived, and its dynamic model is established. The thermo-flexible dynamic response of ANCF composite laminates under thermal conduction, space thermal radiation, and solar radiation is analyzed by numerical simulation. The simulation results reveal the evolution process of the transient temperature field and the phenomenon of thermal-induced vibration, thus confirming that the thermal effects have an important influence on the dynamic behavior of ANCF composite laminates. The research provides a theoretical basis for the ground test of solar panels.

Stability impact on wind turbine blades trailing edge from bonding zone modelling methods

Abstract The trailing edge of wind turbine blade will undergo a large deformation under the action of load, resulting in a higher risk of damage and failure. The finite element analysis modeling method directly affects the simulation result, furthermore impacts the result of blade structure design. Therefore, it is necessary to find out a modeling method, which is capable to reflect the stability of bonding regions more accurately. This paper aims to discuss the influences of different finite element modeling methods on the buckling stability of blade trailing edge. The influences of shell element, tetrahedron element and hexahedron element on the blade stiffness are considered. The bonding region were simulated separately by combining shell element with bonding web, shell element with tetrahedron element and shell element with hexahedron. The influences of different bonding region modeling methods on the trailing edge buckling factor were analyzed by using the eigenvalue buckling analysis method of finite element. The simulation results provided data support for the future validation of the blade trailing edge bonding area modeling method. The results show that, the tetrahedral mesh provides a higher stiffness, followed by the hexahedral mesh, and the adhesive web form has the smallest stiffness. In order to simulate the more realistic stiffness of the adhesive area at the trailing edge of the blade, adhesive web plates can be built in the flange area of the blade root and the core material area of the trial adhesive mold; The direct bonding area can be simulated employing the hexahedron mesh; The tetrahedral mesh has high stiffness and is not suitable for modeling the adhesive area at the trailing edge. Blade simulation modeling can flexibly use different adhesive forms according to actual situations, ensuring the reliability of the simulation model.

A four-node inverse curved shell element coupling MITC method for deformation reconstruction of plate and shell structures

In the field of structural deformation monitoring, the inverse finite element method (iFEM) has significant engineering value as a structural health monitoring technique that provides timely and reliable warnings for shell structures. However, existing inverse finite elements are mainly based on first-order shear deformation theory and kirchhoff-love theory, which are not suitable for deformation reconstruction in plate and shell structures of arbitrary thickness. This study integrates iFEM with the Mixed Interpolation of Tensorial Components (MITC) method to develop a novel four-node quadrilateral inverse curved shell element, named iMICS(inverse Mixed Interpolation Curved Shell)4, aimed at enhancing the accuracy and efficiency of deformation reconstruction in complex plate and shell structures. The method uses the MITC4 shell element as the kinematic framework and applies the least squares variational principle to achieve deformation reconstruction, effectively alleviating shear and membrane locking issues across structures of varying thickness. Numerical examples validate the superior performance of the iMICS4 element, demonstrating its promising application prospects.

Extension of the GISSMO fracture model for thin-walled structures under combined tensile and bending loads

Ductile fracture prediction for thin-walled structures requires computationally efficient simulation tools able to approximately represent the key effects that occur on the sub-thickness scale. Unfortunately, classical shell elements, typically used to model deformation and failure of thin components, are inherently in a state of plane stress and therefore unable to capture the through-thickness stress distribution. This is consequential considering recent studies that demonstrated the differences between fracture in bending vs. in-plane tension. A laterally constrained thin metal plate under in-plane tension is likely to fracture under significantly lower plastic strain than the same plate under bending (with fracture initiating on the tensile side), even though both these conditions are examples of plane strain tension. Under in-plane tension fracture is preceded by a through-thickness neck, and therefore higher stress triaxiality than in the case of plane strain bending, where necking is absent. To account for these differences, we propose an extension of the GISSMO model, which relies on a simple fracture criterion based on stress-dependent fracture strain defined by the user (i.e. fracture locus). The fracture strain is typically determined experimentally using a combination of in-plane tensile tests under varying degree of lateral constraint and shear tests. The proposed extension involves defining a separate fracture locus for bending, also determined experimentally using bending tests. Fracture occurs when the equivalent plastic strain reaches its critical level represented by interpolation between the two bounding cases, i.e. bending and in-plane tension, with a bending index Ω used as an interpolation parameter.

ALTERNATIVE EXPLANATION OF FILLING THE ELECTRONIC LAYERS OF ATOMS OF CHEMICAL ELEMENTS

The article provides a new approach to the formation of periods in Mendeleev's periodic system. Reconfiguration of the periods in the Mendeleev table using the newly proposed formula and the newly proposed quantum states for the outer electron shells of atoms of chemical elements is proposed. Purpose of work: Further development of the alternative theory of creation of electronic shells of atoms of chemical elements in D.I.Mendeleev's table. Results and discussions. The following order of formation of electron layers is proposed: principle quantum number (n), then the quantum state of the electrons forming the electronic configuration of the subperiods (first and second), and only then the remaining quantum orbitals (s, d, f and p). First and second new quantum states and a new formula for calculating the number of electrons in the outer electron shell of element periods and subperiods were proposed. The new level of electronic counting (II) and the new quantum number proposed by us allow to change the understanding of the internal structure of chemical elements without changing the general appearance and order of arrangement of chemical elements in D.I.Mendeleev's table itself, and therefore its contents. An important advantage of the proposed alternative model is that it takes into account and relies on already known, classical data for most of its main operational characteristics and is an extension of this important topic for classical chemistry theory. Therefore, the change in the number of periods, the introduction of a new quantum number in the form of D.I.Mendeleev's table, outwardly it does not differ much, but requires the necessary additional explanation. Concept. The proposed alternative approach to the structure and electronic structure of atomic shells of chemical elements in the periods and groups of D.I.Mendeleev's periodic system was recently developed by the authors and has good prospects for development primarily in the following directions: - identification of possible patterns of changes in the characteristics of chemical and physical properties of elements; - development of an accompanying model of the electronic structure of electronic shells of atoms of chemical elements of the proposed alternative model.