Solid Finite Element Research Articles

Nonlinear thermo-elastic phase-field fracture of thin-walled structures relying on solid shell concepts

The analysis of fracture phenomena of thin-walled structures has been a matter of intensive research in the last decades. These phenomena notably restrict the applicability of slender structures, especially under the influence of temperature. With the aim of achieving reliable prediction of temperature-driven failures in thin-walled structures, this research is concerned with the development of a thermodynamically consistent framework for the coupled thermo-mechanical phase-field model for thin-walled structures using fully-integrated solid shell finite elements. This enables the use of three-dimensional constitutive thermo-mechanical models for the materials. The proposed thermo-mechanical phase-field models are equipped with the Enhanced Assumed Strain (EAS) in order to alleviate Poisson and volumetric locking pathologies. This technique is further combined with the Assumed Natural Strain (ANS) method leading to a locking-free thermo-mechanical solid shell phase-field element. Attention is also paid to the evaluation of the corresponding thermodynamic consistency and the variational formalism leading to the non-linear coupled equations. Moreover, the same degradation function is used for both displacement field and thermal field. The coupled equations are numerically solved with ad hoc efficient solution schemes for non-linear problems. Several numerical examples (straight and curved shells) are provided to assess the reliability of the proposed modelling framework. Representative examples assess stable and unstable crack propagation along with their thermo-mechanical interactions.

A Comparison of Predicted Distortion of a Manifold Fabricated by Laser Powder Bed Fusion Using Solid and Shell Element-based Finite Element Models

This paper compares the predicted distortion of a manifold geometry fabricated by laser powder bed fusion between an established finite element model using solid elements and a newly developed in this paper finite element model using shell elements. The developed finite element models utilized two methods to induce a strain field (inherent strain and analytical thermal methods). The predicted distortions from these models were also compared with experimentally measured distortions. The results showed that the predicted distortion using solid elements is more suitable to predict the buckling effect on the manifold geometry. Despite that, the model using shell elements showed an accurate prediction of distortion in many areas of the manifold, and it proved to be computationally more efficient (2.4 times faster), this model showed lower accuracy in the prediction of distortion generated by buckling. However, shell elements could be used in other applications where the bucking is not the driving mechanism for the prediction of distortion in laser powder bed fusion or in applications where the accuracy of distortion is not a requirement (e.g., support structures).

Analysis of the seismic behavior of traditional Chinese timber structures in the Tang Dynasty

The palace-style timber structure for the Tang Dynasty in China is a world cultural heritage of great value. The East Palace of Foguang temple in Shanxi Province, which is more than 1000 years old, has experienced many earthquakes without collapsing, indicating an excellent anti-seismic performance. The structure has three apparent horizontal layers: the column frame layer with a column foot joint floating directly on the base stone, the bracket complex and beam layer with a relatively high rigidity, and the roof truss layer. This paper performs a dynamic time-history analysis for a typical timber frame in the Tang Dynasty in order to study the seismic performance of the structure and the energy consumption characteristics of the structural layers. A refined solid finite element model is established with the substructure verified by experiments. Dynamic parameters, such as frequency, vibration mode, acceleration response, and displacement response, are studied. The influences of the seismic waves, the vertical load, and the structural configuration are also discussed. The results show that the column foot and head joints give the structure a good deformation capacity. The column layer rotates under seismic action, while the bracket complex layer has a good integrity and moves horizontally with the column head. Column rocking reduces the transmission of vibration energy to the upper layer structure. The multilayer superposition of the bracket complex and the beam layer attenuates the seismic effects. The results reveal that the timber frame column and upper laminated layers have a good earthquake resistance.

Experimental verification of a beam element for thin-walled beams with torsion, distortion, and shear lag

Beam-type elements based on the theories of Euler–Bernoulli, Timoshenko, and Vlasov are widely used in civil engineering. However, shell and solid finite elements are often used when the effects on normal stresses of either shear deformation or distortion are considered important. Numerically validated in an earlier study with finite element models for shell-type structures, the same one-dimensional finite element model is further developed in this study with a low number of degrees of freedom per node that includes all the structural mechanisms without using 3D finite element models. Laboratory testing of an instrumented steel box girder is conducted, to improve validation of the goodness of fit of the finite element model with real structural behavior.

Study of the Hydration Temperature Field in the Hinge Seal Layer for a Large-Volume UHPC Arch Base

For large arch bridges, the sealing hinge layer at the arch footing is critical to the long-term performance and durability of the structure. This study investigated the temperature distribution of the sealing hinge layer inside a large UHPC arch seat during the hydration process in a natural environment, based on a design of a 600-m-span reinforced concrete rigid skeleton arch bridge. A certain suggestion for the design of a large-volume UHPC layer was proposed through the consideration of temperature and age effects of the thermal field solid finite element analysis of early-age UHPC hydration heat. The results show that UHPC has a hydration induction period of 10 h and reaches the peak temperature of 69°C in 20 h. Then, the hydration heat is gradually released in 70 h after pouring. The maximum temperature difference between the core and surface reaches 40°C. The results also show that the early temperature field and heat release rate of UHPC are affected by initial temperature. The actual heat release of some materials of UHPC components at 75 h is equivalent to that at 300 h, and the minimum effective age was found close to 100 h, where the heat release reaches 0.25 of the total heat release. A simplified algorithm for the spatially time-varying non-linear temperature field of the UHPC sealing hinge layer under the influence of temperature and age is proposed, which provides a simple calculation method for the temperature control of the UHPC arch seat during the hydration process in real projects.

Effect of coronal fracture angle on the stability of screw fixation in medial malleolar fractures: A finite element analysis.

Malleolar screw fixation is the most widely used treatment method for medial malleolar (MM) fractures. Here, although buttress plate fixation is advocated for vertical MM fractures, the angular discrimination between oblique and vertical MM fractures is still not fully understood. The purpose of this study is to test the adequacy of screw fixation in MM fractures with different angles and determination of a 'critical fracture angle' to guide surgeons in the decision-making for screw fixation for MM fractures by utilizing an advanced engineering simulation approach. In addition to loading of the healthy tibia structure, various cases of the MM fracture double screw fixation (14 simulation scenarios in total with fracture angles between 30° and 90°, in 5° increments) were considered in this research and their static loading conditions just after fixation operation were simulated through nonlinear (geometric and contact nonlinearity) finite element analysis (FEA). Patient-specific computed tomography scan data, parametric three-dimensional solid modelling and finite element method (FEM) based engineering codes were employed in order to simulate the fixation scenarios. Visual and numerical outputs for the deformation and stress distributions, separation and sliding behaviours of the MM fracture fragments of various screw fixations were clearly exhibited through FEA results. Minimum and maximum separation distances (gap) of 3.75 and 150.34 µm between fracture fragments at fracture angles of 30° and 90° were calculated respectively against minimum and maximum sliding distances of 25.87 and 41.37 µm between fracture fragments at fracture angles of 90° and 35°, respectively. The FEA results revealed that while the separation distance was increasing, the sliding distance was decreasing and there were no distinct differences in sliding distances in the scenarios from fracture angles of 30°-90°. The limitations and errors in a FEA study are inevitable, however, it was interpreted that the FEA scenarios were setup in this study by utilizing acceptable assumptions providing logical outputs under pre-defined boundary conditions. Finally, the fracture healing threshold for separation and/or sliding distance between fracture fragments was assigned as 100 µm by referring to previous literature and it was concluded that the screws fixed perpendicular to the fracture in a MM fracture with more than 70° angle with the tibial plafond results in a significant articular separation (>100 µm) during single-leg stand. Below this critical angle of 70°, two screws provide sufficient fixation.

Solid-shell approach based on first-order or higher-order plate and shell theories for the finite element analysis of thin to very thick structures

A new solid-shell approach dedicated to thin to very thick structures is presented. Plate or shell displacement fields are directly applied on a solid finite element model which contains several elements through the thickness. Any plate or shell theory based on kinematic assumptions can be used, in this study three theories have been considered. The classical first-order theory, the modified first-order theory and a higher-order theory lead to the FOSS, the MFOSS and the HOSS models respectively. Kinematic relations are imposed at nodes to meet through-the-thickness plate or shell displacement fields. From a numerical point of view, linear equations are applied on the assembled finite element model. The methodology relies on the slave and master nodes technique. Slave nodes are eliminated, leading to a reduction of the model size. Two examples are presented: a clamped square plate under distributed loading and a quarter of cylinder under pressure. For the thin and thick cases, displacements and stresses are observed. The FOSS model leads to unsatisfactory results. The HOSS model gives excellent results in the thin as well as the thick cases, by comparison with the solid approach. The MFOSS model is satisfactory for thin structures and leads to moderate errors in the thick case. This approach is also efficient from a computational cost point of view.

Development and seismic performance improvement of hybrid damping self-centering braced frame

A novel hybrid damping self-centering brace (HD-SCB) with friction dampers and viscoelastic dampers is proposed in this paper. The ratio of the frictional force and viscous force in the HD-SCB system can be easily changed. Through a solid finite element model, the HD-SCB is found to have a controllable velocity-based energy dissipation capacity. A series of the HD-SCB frames (HD-SCBFs) are designed with a presented design method, which considers the energy dissipation equivalent and the damping force equivalent. 2 groups of the scaled ground motions with or without a velocity pulse are selected, and the pulse characteristics are identified by calculating the pulse indicator of each record. A novel higher mode analysis method is proposed to observe the participation of the higher mode. Through comprehensive analyses on the HD-SCBFs, it can be found that adding viscoelastic dampers can significantly reduce the displacement response of the higher floor because the higher mode effect is weakened. The ratio of the frictional damping force to the viscous damping force of the HD-SCB is suggested to be 0.25–0.50. In this case, acceleration response can be reduced by 25% without amplifying the base shear.

Quantitative analysis of extra load-carrying mechanisms to prevent progressive collapse of reinforced concrete buildings

Occurrence of progressive collapse events invariably leads to significant economic and human-life losses. Progressive collapse analysis and design of building structures have become a research hotspot worldwide. Existing studies have proved that development of extra load-carrying mechanisms could significantly improve the resistance of structures to progressive collapse. However, limited research has been conducted to quantitatively analyze these mechanisms. This study proposed a new and unified division method for mechanisms for resisting progressive collapse; furthermore, it provides a basis for their quantitative analysis. In addition, the progressive collapse behavior of a 1/3-scaled two-story, one-bay-by-two-bay reinforced concrete (beam–slab–column) frame with an edge column lost was experimentally investigated. Additionally, a 3 D solid finite element model was established and validated based on the test results. The effects of different extensive parameters, including ideal lateral constraints, slab thickness, and beam–slab interaction, on each resisting mechanism were quantitatively investigated. Finally, a new simple method for predicting the first peak load was proposed based on the contribution of each mechanism. The results from the simple method were in agreement with the simulation results of beam–slab–column structures.

Time harmonic analysis of concrete arch dam-reservoir systems by utilizing GN high-order truncation condition

In present study, the dynamic analysis of concrete arch dam-reservoir systems is formulated by FE-(FE-TE) approach. In this technique, dam and reservoir are discretized by solid and fluid finite elements. Moreover, the GN high-order condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model. The formulation is initially explained in details. Subsequently, the response of idealized Morrow Point arch dam-reservoir system is obtained for two fully reflective and absorptive reservoir bottom/sidewalls conditions for all three types of excitations. Different Orders of GN condition are considered and convergence process is evaluated. Furthermore, the results are compared against exact solutions which are based on rigorous FE-(FE-HE) approach. It is shown that the technique converges prior to beginning of instability problems which is known to exist for high orders in GN condition. It must be emphasized that although time harmonic analysis is considered in the present study, the main part of formulation is explained in the context of time domain. Therefore, the approach can easily be extended for transient type of analysis.

Numerical simulation of the in-plane lateral response of RC infill frames using a FEM-DMEM modelling approach

Reinforced concrete frame structures incorporating masonry infills are common forms of construction and can be found in many seismic regions of the world. Often these frames are designed for gravity loads only and neglect the effects of the non-structural masonry infill walls. A detailed simulation of infill frames requires refined mesoscale models to capture the behaviour of the reinforced concrete frame, the masonry infill and their complex nonlinear interaction. One of the most efficient modelling approaches is the Discrete Macro Element Model (DMEM), which has the advantage of providing a geometrically consistent description of the infill-frame interaction with limited computational effort compared to refined finite element models. In the original formulation of the DMEM approach, the frame is simulated by means of 1D beam/column elements interacting with the macro-elements, simulating the infills, by means of discrete interfaces. In this paper, a hybrid modelling strategy is developed using the commercially available software ABAQUS. The frame is modelled by means of nonlinear 3D solid finite elements, while the infills are simulated by adopting the DMEM model i.e. macro-elements. Unlike previous models, this model allows the novel simulation of the shear behaviour, which highly governs the lateral resistance, between the frame and infill via 2D continuum contact elements. The capability of the proposed model to simulate the non-linear response and failure mechanisms of masonry infill frames is demonstrated by comparing the numerical results to published experimental results. The results showed that the model predicted the ultimate horizontal load carrying capacity with an accuracy level of 95% and the predicted failure modes were in agreement with the experiment.

A new solid-beam approach based on first or higher-order beam theories for finite element analysis of thin to thick structures

A new solid-beam approach devoted to thin to very thick beam-like structures is proposed. To meet the beam displacement fields, kinematic relations are directly applied on the solid finite element model which contains several elements through the thickness and width. It is possible to use any beam theory based on kinematic assumptions and three theories are considered in this paper. The classical first-order beam theory, the modified first-order beam theory and a higher-order beam theory lead to the FOSB, the MFOSB and the HOSB models respectively. Linear equations due to kinematic relations are imposed at slave nodes to meet displacement fields throughout the cross-section, resulting in a reduction of the model size. Two examples are presented: a straight beam and a curved beam under distributed loading. The FOSB model gives unsatisfactory results. For a thin beam, the MFOSB model is adequate but leads to moderate errors in the thick case. Compared to the solid model, the HOSB model offers excellent displacements and stresses in thin and thick cases. The final size of these solid-beam models is slightly larger than that of an approach with classical beam elements.

Test and Theory for a Refined Structural Model of a Hirth Coupling

Abstract Hirth coupling transmits high torques in the rotating assemblies of compressors and turbines. Their mating surface contacts cause local changes in lateral shaft stiffness. This is affected by the teeth geometry, contact surface area, coupling preload, and surface finish at the contact faces. Industry practice ignores localized lateral flexibility from the Hirth coupling, or is guided by limited experience-based rules of thumb. The authors provide a novel modeling approach utilizing 3D solid finite elements which accounts for contact deformations, intricate interface teeth geometries, stress concentration, and surface finish. This provides an increased accuracy localized stiffness model for the Hirth coupling, to improve rotordynamic response predictions. Free–free natural frequencies of a test rotor including a Hirth coupling are experimentally measured. The rotor is instrumented with strain gauges for preload force measurements, and the Hirth coupling contacting surface profiles are measured with a stylus type surface profiler. A GW contact model is obtained from the measured surface profiles. An iterative computation algorithm is utilized to calculate Hirth coupling contact stiffness and contact pressure at the complex-shaped contact surfaces. Predicted and measured natural frequencies are compared versus preload.

Analysis of unreinforced and reinforced tubular T-joints structures with open source finite element software

Tubular Joints play quite a vital role in most marine structures. It is obvious that having full control about the capacity and strength of tubular joints would be very worthy to have good knowledge about the total performance of the structure. In recent years, the application of the finite element method has become very popular in the analyses of different types of welded circular tubular joints and many commercial and open-source FE systems have been profoundly involved in these regards. Most of these software shares so much in common that it is difficult to differentiate them. This study was performed to investigate and report the usefulness of the open-source software programs in implementing finite element modeling for design applications. In this regard, with aid of the open-source finite element package Code_Aster and its user-friendly interface Salome-Meca, the behavior of reinforced and unreinforced T-joint specimens subjected to axial brace load with different geometry and material property has been studied. In addition, different types of shell and solid finite elements with various mesh densities are considered in this research. In order to overlap the outcomes, the numerical results of this research are present in terms of load-ovalization curves along with the results of other references. Due to mesh sizes and the element types, 144 different simulations have been performed on 12 different specimens. The results show that Code_Aster can satisfactorily predict the nonlinear static behavior of reinforced and unreinforced joints under both tension and compression load. Hence, Code_Aster can be used as a reliable tool for the evaluation and analysis and design of complex offshore joints.

An efficient multiphysics solid shell based finite element approach for modeling thin sheet metal forming processes

The main objective of this paper is to provide a numerical approach to study thin sheet metals involved in multiphysics manufacturing processes. The proposed approach also accounts for anisotropic plastic deformations in the context of modeling of deep drawing process. In this work, different constitutive models are implemented with a prismatic solid shell element to simulate these applications. Moreover, a new element assembly technique has been developed to permit the assembly of prismatic elements in a tetrahedral element-based finite element code. This technique splits the prism into multiple tetrahedral elements in such a way that all the cross terms are accounted for. The numerical approach has been validated using multiple tests that involve different non-linearities: geometric, material and contact. Then, more complex sheet metal processes have been simulated. The performance of the solid shell element with one element through the thickness is very comparable to the results obtained with more refined mesh of a tetrahedral element. This reduction in the number of elements accelerates the simulation, especially in the deep drawing problem and the coupled magnetic-mechanical simulation used for the magnetic pulse forming process. • Solid shell finite element implementation in tetrahedral based finite element software. • Prism division algorithm into multiple overlapping tetrahedral elements. • Solid-shell element showed better performance than MINI element in modeling thin structures problems. • Incorporate anisotropic plastic behavior in the simulation of deep drawing process. • Electromagnetic pulse forming simulation using solid shell element reduces time of simulation and maintain good accuracy.

Impact Response Analysis of Panel with Partial Acoustic Black Hole Supported by Nonlinear Concentrated Springs

This paper describes vibration analysis using Finite Element Method with Model Strain Energy Method for steel panel connected by nonlinear concentrated springs under impact load. The panel is composed of steel layer with a partial acoustic black hole having a damping layer in the plate edge. The Acoustic Black Hole has a viscoelastic damping layer. Finite elements for the nonlinear springs with hysteresis are expressed and are connected to the panel modeled by linear solid finite elements in consideration of complex modulus of elasticity. We calculated modal loss factors and transient responses including coupled motions between the non-linear springs and the panel. From the dominant eigen modes and the time histories, we clarified effects of a partial acoustic black hole having a damping layer in the plate edge and non-linear springs on the nonlinear damped responses.

Eigenvalue Analysis and Impact Response Analysis for T-shaped Structures with New Acoustic Black Hole Including Residual Thickness Supported by Nonlinear Concentrated Springs

This paper describes analysis using finite element method with Model Strain Energy Method for steel structures having a T-shaped cross section supported by nonlinear concentrated springs under impact load. An edge of the rib plate in the T-shaped structure has an Acoustic Black Hole with residual thickness. A viscoelastic damping layer is covered on the acoustic black hole. Finite element for the nonlinear springs with hysteresis are expressed and are connected to the T-shaped structures modeled by linear solid finite elements in consideration of complex modulus of elasticity. We calculated modal loss factors and transient responses using the eigen modes including coupled motions between the non-linear springs and the T-shaped structures. From the dominant eigen modes and the time histories, we clarified effects of an Acoustic Black Hole with residual thickness and nonlinear springs on the nonlinear damped responses.

Finite Element Analysis of Damping Characteristics of Flat Plate with residue thicknesses and half crater new type acoustic black holes

This paper deals with vibration damping analysis using finite element method with Model Strain Energy Method for flat plate having new type acoustic black holes. The new acoustic black holes have half craters and residue thicknesses on both sides of the flat plate. Viscoelastic vibration damping materials are laminated over the acoustic black hole. The flat plate is fixed on two edges where the acoustic black hole does not exist. The damping layer is modeled by linear solid finite elements in consideration of complex modules of elasticity. We calculated modal loss factors and eigenmodes of the models. We clarified effects of the new acoustic black hole on the modal damping for each eigenmode. The results show that having a residue thickness provides damping in the low-frequency range. It was also found that having a residue thickness increases the damping effect.

Fracture prediction for square hollow section braces under extremely low cycle fatigue

This paper examines the extremely low cycle fatigue (ELCF) fracture of concentrically loaded square hollow section (SHS) braces subjected to cyclic loading. Numerical analyses are presented for both individual bracing members and bracing members integrated into concentrically braced frames (CBFs). The behaviour of the individual members was predicted using solid finite element (FE) simulations that employed a ductile fracture model and a nonlinear damage evolution rule. The solid FE model, which was validated using data from experiments, could adequately predict both the hysteretic response and the ELCF fracture cracking process. The coupled effects of instabilities (i.e. local and global buckling) and fracture on the ELCF performance of the braces were assessed, and the rotation capacity prior to fracture was quantified. This quantified rotation capacity was then incorporated into fibre-based FE models of CBFs as a member-level fracture criterion. The structure-level simulations were able to accurately capture the complex interactions between the frame components, i.e. the columns, beams, brace–gusset–plate​ connections and beam-to-column connections, and hence replicate the overall behaviour of CBFs, specifically, two-storey chevron braced frames. The influence of cross-section and member slenderness was evaluated and the importance of considering both in the development of cross-section slenderness limits was highlighted. The combined member- and structure-level simulation approach is proposed as an accurate and efficient means of assessing the seismic performance of CBFs.

GEOMETRICALLY NONLINEAR DEFORMATION AND BUCKLING OF SMOOTH AND FACETED SHELLS

Practical using of curvilinear shape shells is related with significant problems during their production especially for metal structures. Therefore during such shells production curvilinear shape is replaced by faceted. Realization of this method when designing needs additional investigations performing of faceted shells bearing capacity on the basis of appropriate numerical calculation method using. Problems of solving such tasks are practically not displayed in the literature. Break-in of the middle surface affect significantly to the shell stress-strain state. Accounting of temperature fields’ influence in the problems of their stability complicates their behavior research even more. In this paper the research results comparing analysis of static problems about smooth and faceted shells nonlinear deformation and stability under mechanical loads is presented. The problem is solving with using of software that are based on the finite element method: by method that realized the moment finite-element scheme and using software package LIRA. The solving method that used the moment finite-element scheme is based on the geometrically nonlinear equations of the 3D theory of thermoelasticity without application of theory of shells simplifying hypothesis and on the applications of the universal three-dimensional solid finite element.