Modeling Beam–Solid Finite Element Interfaces: A Stabilized Formulation for Contact and Coupled Systems

A finite element formulation is developed including the fully coupled electrical-structural constitutive relations. An effort has been made to develop the most general formulation applicable to laminated composite plates with inclusion of piezoceramic sensors/actuators. To this end, the von Karman large deflection theory was included, due to the results obtained from the experiments conducted. Solution of the large deflection problem lead to an electrical-structural coupled tangent stiffness, which is believed to be the first time reported in the literature. paper presents comparison of the finite element simulation to experimental results for both static and dynamic piezoceramic sensors in addition to dynamic piezoceramic actuation. INTRODUCTION Piezoelectric material maintains a complex and intricate relationship between several physical sciences such as materials, thermal, electric fields, and elasticity. Evidence of the piezoelectric's complexity can be demonstrated by the seemingly continuous research conducted since its discovery in 1880 by Pierre and Jaques Curie. Much of the research set out to determine analytical models describing the piezoelectric phenomenon and lead to discrete devices such as extremely sharp crystal filters and stable oscillators. Mindlin developed classical methods describing the analysis on waves and vibrations in isotropic elastic plates concurrently with high frequency vibration of crystal plates. Allik and Hughes developed a solid, or three dimensional, finite element to model transducers and crystal oscillators. However, given that smart structures typically consist of thin piezoelectric layers attached to structures that are several orders of magnitude greater in thickness, the solid finite element formulation leads to an inherently inefficient process in which to model the complete physical structure. Subsequently Tzou and Tseng * Graduate Student, Student member AIAA. t Professor, Associate Fellow AIAA. This paper is declared a work of the U.S. Government and is not subject to copy right protection in the United States. formulated a new thin piezoelectric solid finite element in the form of shell and plate elements. When considering piezoelectrics in conjunction with structural members, linear piezoelectric theory simplifies the piezoelectric effect. Linear piezoelectric theory assumes an isothermal adiabatic process and quasi-static electric field equations. research presents a comparison of the fully coupled electricalstructural finite element analysis of an isotropic panel with a surface mounted piezoelectric patch to experimental results. PIEZOELECTRIC RELATIONS Piezoelectric material inherently possesses coupling between electrostatics and structural dynamics. Linear piezoelectric theory yields an intrinsically coupled pair of piezoelectric constitutive equations. One describes the direct piezoelectric effect where the state of strain gives rise to an electric polarization, and the other describes the converse effect where an applied electrical field develops a state of strain. For a thin piezoelectric layer, the following constitutive relations result from linear piezoelectric theory (1)

This study is focusing on the finite element simulation of low velocity impact applied to glass fiber-reinforced composites. Elasto-visco-plasticity is adopted taking into account strain rate effect, with isotropic hardening. To avoid numerical locking, hexahedral solid shell finite element SS is developed. The formulation is based on the mixed Assumed Natural Strain (ANS) and the Enhanced Assumed Strain (EAS) methods. A geometrical non linear condition is applied. The finite element is implemented in UEL subroutine via the commercial software ABAQUS/Standard. The numerical element proved its efficiency comparing to conventional element and previous experimental results in (Mars et al. 2018). Numerical simulations with solid element are conducted using Abaqus/standard via user material UMAT subroutine. In terms of computation time, the solid shell element is less time consuming when comparing to conventional solid element. This is due to the fact that a single element through the thickness direction is adopted. Element efficiency is assessed for various fibers contents.

Piezocomposites are attracting widespread interest since they can offer greater flexibility and better performances in specific applications with respect to traditional piezoelectric wafers. Design of piezocomposites requires accurate homogenisation models for the prediction of the equivalent electro-mechanical properties. In macro-scale models of structures with piezocomposite transducers, these properties are adopted in order to avoid the complexity of the piezocomposite microstructure. In the case of smart structures the accurate modelling of the actuation and the response of the structure is of primary importance. If classical structural finite elements are not sufficiently accurate, higher order or solid elements should be adopted. Thanks to adaptation or mixed-dimensional methods, it is possible to adopt computationally expensive higher order or solid elements only in some sub-domains of the structure. In this work, the modelling of smart structures equipped with thin piezoelectric transducers is considered in a multi-scale framework. Micromechanical homogenisation models are developed and employed for the prediction of the equivalent properties of piezocomposites. A micromechanical model based on the concept of inclusion is proposed to investigate the influence of the shape of the inclusions, of the constituent materials and of the polarisation on the equivalent properties. It has been found that fibre-shaped inclusions should be considered in order to obtain piezocomposites with strong piezoelectric effect and to have at the same time high direction-dependence. The equivalent properties of Macro Fiber Composites are determined via the Asymptotic Homogenisation Method (AHM) with an analytical solution and with a numerical solution via FEM which takes into account the effect of the electrodes. AHM analytical solution is adopted to investigate the effect of the material properties of the matrix on the overall piezocomposite. Results indicate that low values of the Young's modulus and of the Poisson's ratio yield high directional dependence in the piezoelectric properties. A laminated design with anisotropic layers and a piezocomposite layer is investigated via UFM. A configuration with maximum directional dependence in terms of equivalent piezoelectric strain constants is proposed, whereas maximum directional dependence in terms of piezoelectric stress constants is proved to be not achievable with such a design. Hierarchical finite elements for structural analyses based on a Unified Formulation (UF) by Carrera are developed and coupled via the Arlequin method proposed by Ben Dhia. Solid, plate and beam finite elements for mechanical and for piezoelectric problems are presented. Via UF, higher order and piezoelectric elements can be formulated straightforwardly. These elements are combined in variable kinematic solutions in the Arlequin framework. Higher-order elements are adopted locally where the stress field is three-dimensional, whereas the remaining parts of the structure are modelled with computationally cheap lower-order elements. Two electro-mechanical coupling operator for the Arlequin method in the context of piezoelectric analyses are proposed. Results are validated towards monomodel solutions and three-dimensional analytical and numerical reference solutions. Accurate solutions are obtained reducing the computational costs

The use of laminated glass (LG) as a structural material for load-bearing components within buildings has been growing over the last decades. LG can be obtained by bonding two or more pieces of glass by means of polymeric interlayers (e.g., poly vinyl butyral – PVB). This building process gives LG elements a huge advantage over the same ones made of fully monolithic glass with respect to safety, since after breakage the fragments usually remain attached to the interlayer, reducing the risk of injuries. As LG members usually present a high slenderness, they are susceptible to flexural buckling under compression, requiring specific calculation methods and verification procedures in order to guarantee appropriate and safe structural performance. Compared to literature, this work presents a novel approach that is focused on the prediction of the elastic critical buckling load of LG columns without any lateral restraints at the tensioned edges. The buckling loads of LG columns have been determined using Finite Element Method, generally using shell elements, or analytical models. Usually, such approaches make use of the concept of effective thickness, in which the thickness of a monolithic element with equivalent bending properties in terms of stress and deflection is employed. However, the effective thickness approach is either difficult to apply or inaccurate. Therefore, this work presents an efficient and accurate approach to evaluate elastic critical buckling loads of LG columns applying Finite Prism Method (FPM). The accuracy of the proposed approach is assessed comparing the results obtained using solid finite element and analytical models for fully monolithic glass columns, as well as LG columns composed by multiple glass layers.

In this technical note, a consistent finite element formulation of the Hyperstatic Reaction Method (HRM) for tunnel linings design is proposed by introducing a variational consistently linearized formulation. It permits to consider a nonlinear interaction between a lining structure and the surrounding ground. Recent advances of the HRM in regard to the consideration of the nonlinear response of the segmented tunnel lining exposed to design loads use an iterative algorithm for solving the nonlinear system of equations. In the proposed Variationally consistent Hyperstatic Reaction Method (VHRM), a distributed nonlinear spring model representing the interaction between the lining and the ground soils is considered in a variationally consistent format. Computing the tangential spring stiffness via consistent linearization, and using Newton‐Raphson iteration, requires significantly smaller number of iterations as compared to the original HRM model based on nodal springs. Furthermore, the method is applicable for simulations using solid finite elements (2D and 3D), as well as beam or finite shell elements, respectively.

To analyse the behaviour of thin structures of dielectric elastomer (DE) material a solid shell finite element is presented. The main characteristics of DEs are a non‐linear hyper elastic behaviour, the quasi‐incompressibility, and the ability to transform electric energy into mechanical work. Applying a voltage to thin DE structures may produce large elongation strains of 120‐380%. These large strains, the efficient electro‐mechanical coupling, and the light weight make DEs very attractive for the usage in actuators. Thus, there is a need for detailed research. With respect to the electro‐mechanical coupling a constitutive model is presented. An electric stress tensor and a total stress tensor are introduced by considering the electrical body force and couple in the balance of linear momentum and angular momentum, respectively. The governing equations are derived and embedded in the solid shell formulation. The element formulation is based on a Hu‐Washizu mixed variational principle using six independent fields: displacements, electric potential, strains, electric field, mechanical stresses, and dielectric displacements. It allows large deformations and accounts for physical nonlinearities to capture two of the main characteristics of DEs. The shell element could be applied for the modelling of arbitrary curved thin structures. The ability of the present element formulation is demonstrated in several examples. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

An improved model for the dynamic analysis of plates stiffened by parallel beams

Crush simulations of composite energy absorbing structural systems

A shaft is modelled using three-dimensional solid finite elements. The shear-deformation and rotary inertia effects are automatically included through the three-dimensional elasticity formulation. The formulation allows warping of plane cross-sections and takes care of gyroscopic effect. Unlike a beam element model, the present model allows the actual rotor geometry to be modelled. Shafts with complicated geometry can be modelled provided that the shaft cross-section has two axes of symmetry with equal or unequal second moment of areas. The acceleration of a point on the shaft is determined in inertial and rotating frames. It is found that the finite element formulation becomes much simpler in a rotating frame of reference that rotates about the centre-line of the bearings with an angular velocity equal to the shafts spin speed. The finite element formulation in the above frame is ideally suited to non-circular shafts with solid or hollow, prismatic or tapered sections and continuous or abrupt change in cross-sections. The shaft and the disc can be modelled using the same types of element and this makes it possible to take into account the flexibility of the disc. The formulation also allows edge cracks to be modelled. A two-dimensional model of shaft disc systems executing synchronous whirl on isotropic bearings is presented. The application of the two-dimensional formulation is limited but it reduces the number of degrees of freedom. The three-dimensional solid and two-dimensional plane stress finite element models are extensively validated using standard available results.

In the paper, the results of the analysis of shear stiffness of steel roof panel are represented. Steel panels are used in the roofs of workshops with increased heat, gas and dust emissions. In the paper, there was analyzed the possibility of accounting for steel panels as fastening elements for the upper belt of the trusses, as well as the possibility of taking into account the roof panels in the spatial framework, as elements of the shear disk of the roofing through which efforts are transferred from one frame to another. The shear stiffness of the panel was determined using the FEMAP 11.1.2 software package, when the panel was modeled by solid finite elements. In the software complex Lira-SAPR 2017, the calculation was performed using beam (for beams and edges of the roof panel) and plate (for steel sheet) finite elements. A good agreement of the results obtained with the use of beam and plate finite elements with the results obtained with the use of solid finite elements was found. The optimal plate finite element mesh of the sheet was determined.

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

Accurate modeling of many engineering systems requires the integration of multibody system and large deformation finite element algorithms that are based on general constitutive models, account for the coupling between the large rotation and deformation, and allow capturing coupled deformation modes that cannot be captured using beam formulations implemented in existing computational algorithms and computer codes. In this investigation, new three-dimensional nonlinear dynamic rubber chains and belt drives models are developed using the finite element absolute nodal coordinate formulation (ANCF) that allows for a straight forward implementation of general linear and nonlinear material models for structural elements such as beams, plates, and shells. Furthermore, this formulation, which is based on a more general kinematic description, can be used to predict the cross section deformation and its coupling with the extension and bending of the belt drives and rubber chains. The ANCF cross section deformation results are validated by comparison with the results obtained using solid finite elements in the case of a simple tension test problem. The effect of the use of different linear and nonlinear constitutive laws in modeling belt drive mechanisms is also examined in this investigation. The finite element formulation presented in this paper is implemented in a general purpose three-dimensional flexible multibody algorithm that allows for developing detailed models of mechanical systems subject to general loading conditions, nonlinear algebraic constraint equations, and arbitrary large displacements that characterize belt drives and tracked vehicle dynamics. The successful integration of large deformation finite element and multibody system algorithms is shown to be necessary in order to be able to study the dynamics of complex tracked vehicles with rubber chains. A computer simulation of a three-dimensional multibody tracked vehicle model that consists of twenty rigid bodies and two flexible rubber chains is used in order to demonstrate the use of the formulations presented in this investigation.

ABSTRACT: The goal of this paper is to present recent developments aimed at improving computational efficiency and extending the range of material applicability of a 2D/3D FDEM geomechanical simulation software. Firstly, a hybrid FEM-FDEM logic was devised to allow for user-defined regions of the domain to be modeled as a continuum, while the remainder is captured by the FDEM formulation with an intrinsic cohesive zone model explicitly capturing fracturing. Benchmarking results indicate simulation speed-ups of up to 48x when using the new logic versus the traditional full FDEM approach. Secondly, the finite element formulation was enhanced with elasto-plastic constitutive models based on Drucker-Prager and Mohr-Coulomb failure criteria, effectively broadening the range of applicability to materials that exhibit irreversible damage processes under load without breaking. These developments were initially verified by comparing simulated stress distributions against analytical solutions for select boundary value problems. Practical validation of the novel FDEM formulation was achieved by capturing the variation of critical failure mechanism observed in a slope as a function of the type of rock mass jointing. The factors of safety computed with the strength reduction method compared very well with those reported in the literature for commercially available programs based on DEM and FEM. Finally, a direct comparison between FEM-based, elasto-plastic and FDEM-based, brittle-fracture models is presented for the case of a homogeneous rock slope. 1. INTRODUCTION The finite-discrete element method (FDEM) is a numerical method originally introduced by Munjiza et al. (1995) as a means of combining principles of continuum mechanics, such as the theory of elasticity and non-linear fracture mechanics, with discrete element algorithms to model fracture, fragmentation, and failure of cementitious materials and rocks. Building upon Munjiza's pioneering work, FDEM has been further developed by a multitude of research groups and organizations worldwide, and applied to a variety of rock mechanics and rock engineering problems where consideration of brittle fracturing processes is critical. Over the years, developments of FDEM have focused on several major areas of interest including (i) improvement of the core algorithms for deformation, fracture, interaction, and contact detection (e.g., Lei et al., 2016, Fukuda et al., 2021, Cai et al., 2023), (ii) incorporation of multi-physics capabilities to account for hydraulic and thermal effects (e.g., Yan and Jiao, 2018, Yan et al., 2019, Munjiza et al., 2020), and (iii) reduction of simulation run times by parallel computing (e.g., Lei et al., 2014; Lisjak et al., 2018; Fukuda et al, 2019). In the classic implementation of FDEM (Munjiza, 2004), the numerical representation of fractures is achieved by an intrinsic cohesive zone model (ICZM). With this approach, zero-thickness cohesive crack elements are inserted (at the beginning of the simulation) across pairs of adjacent solid finite elements throughout the entire modelling domain. All irreversible ("plastic") deformations are concentrated in the form of yielding and breakage of the interfaces between the solid finite elements, which remain elastic.

Modern software packages for calculating buildings and structures for various types of action make it possible to simulate the structure and its elements in sufficient detail and to reflect adequately the behavior of this structure. However, detailed simulation with the use of solid finite elements requires a large amount of computing time to perform calculations. This problem can be solved by moving from solid finite elements to bar elements. At the same time, it is necessary to verify the bar calculation models. The article compares the calculation results of a reinforced concrete column simulated in two ways: with the use of solid finite elements based on the actual reinforcement and with the use of bar finite elements. The concrete material for the reference model is specified using a Continuous Surface Cap Model nonlinear model implemented in the LS-DYNA software package. This model reflects the non-linear behavior of concrete and enables to consider the joint behavior of concrete and reinforcing bars. The diagrams of concrete behavior in the bar model are adopted in accordance with SP 63.13330.2012 “Concrete and reinforced concrete structures. Revised edition of SP 52-101-2003”. The study compares the results obtained by the breaking load value and the fracture pattern of the column under consideration.

In this paper, the structure of cylindrical shell with a reinforced circular cutout using combination model of solid element and shell element was analyzed by Finite Element Method (FEM) simulations. Multipoint constraint (MPC) method is mainly used to solve the connection between solid element and shell element when considering the calculation accuracy and efficiency of the model. The combination model of solid and shell element is established in ANSYS, and has been compared to the model of shell element and the model of solid element. The result showed that in the aspects of the stress distribution of the pressure hull near the cutout, buckling behavior of the structure and its instability response, the combination model of solid and shell element was almost equal to the others, it is convincible as well as possessing merits of other models.