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In this study, we present alternative viscoelastic models for materials developing large strains. The novelty of these models is the definition of isochoric strain components, from which we numerically calculate isochoric strain rates. The proposed models differ from the most usual frameworks present in the literature, namely Köner–Lee decomposition models, hereditary integral models and thermodynamically consistent models. The last mentioned framework also uses the Flory's multiplicative strain decomposition, but not in the same way proposed here. Our models are developed for solid mechanics and their time evolution is done through finite differences, simplifying the algorithmic tangent viscoelastic constitutive tensor and the consideration of strain rate-dependent viscosity. Using simple examples, we show that using finite difference for isochoric strain rate evolution does not introduce volumetric changes in purely distortional viscoelastic situations and vice versa. We also present examples related to experimental results, including nonlinear viscoelastic response. Finally, we present examples that show how viscoelastic materials with instantaneous response may not provide satisfactory damping for some structural sets and a comparison of our models with important classical models. [ABSTRACT FROM AUTHOR]

When writing movement equations in stresses for continuous media, it makes no difference whether the media are solid or fluid. The fundamental difference in the solution of these two problems relies on the respective constitutive laws. For solids, shear stresses are related to shear strains, resulting the Navier–Cauchy equation. For fluids, shear stresses are related to the time rate of shear strains, resulting in the Navier–Stokes equation. For solid and fluid isothermal problems, the pressure is related to the volumetric change. Based on hyperelastic solid mechanics equations, we present an alternative total Lagrangian unified model to simulate free surface compressive viscous isothermal fluid flow and simple viscoelastic solids. The proposed model is based on the deformation gradient multiplicative decomposition, which enables to establish a consistent Lagrangian constitutive law for quasi-Newtonian and non-Newtonian fluids, as well as for Kelvin–Voigt-like solids. The proposed constitutive model and the resulting positional prismatic finite element formulation are explored in numerical examples. [ABSTRACT FROM AUTHOR]

The Flory's decomposition is an important mathematical tool used to write hyperelastic constitutive models. As far as the author's knowledge goes, it has not been used to write plastic flow directions in elastoplastic models and this study is an opportunity to introduce this simple strategy in so important subject. Adopting this decomposition it is possible to write an alternative total Lagrangian elastoplastic framework for finite strains with simple implementation and good response. Using Flory's decomposition, strains are split into one volumetric and two isochoric parts. The volumetric part is considered elastic along all strain range and isochoric parts are treated as elastoplastic, i.e., the isochoric plastic flow direction is directly defined by the Flory's decomposition. Assuming this plastic flow direction it is not necessary to employ the classical Kröner-Lee multiplicative decomposition to consider elastic and plastic parts of finite strains. The proposed model is implemented in a 3D geometrical nonlinear positional FEM code and results are compared with literature experimental and numerical data for validation purposes and applications. [ABSTRACT FROM AUTHOR]

A flexible actuator finite element is developed and applied for the modelling of spatial mechanisms present in several industrial applications. A total Lagrangian framework is employed for the development of the finite deformation dynamic equilibrium using solid-like shell and 3D frame finite elements. Exploiting the total Lagrangian aspect of the formulation, the actuator motion is imposed by controlling the element reference configuration. It has the advantage of retaining the actuated bar flexibility, an important factor when simulating flexible mechanisms, and not requiring special treatments as constraint enforcement impositions. As the employed elements use alternative nodal parameters such as positions and generalized vectors to describe their kinematics, a treatment on the introduction of rotational connections—spherical, revolute and pinned joints—largely present in actuated mechanisms, is developed. The nonlinear equations of motion are solved by the Newton–Raphson method. Examples are presented to evaluate the proposed flexible actuator finite element regarding its dynamical behaviour in mechanisms where its use is of importance. [ABSTRACT FROM AUTHOR]

One of the most employed strategies in finite element analysis of fluid-structure interaction (FSI) problems involves using an arbitrary Lagrangian-Eulerian (ALE) method for the fluid, requiring an additional step to the partitioned coupling algorithm: the dynamic mesh moving. Mesh moving techniques need to avoid excessive element distortion or inversion. In this work, we develop a partitioned FSI algorithm for large displacement shell structures-incompressible flow interaction analysis using the finite element method (FEM). The coupling is performed by a block Gauss-Seidel implicit approach and the fluid mesh is updated by a linear Laplacian smoothing. To save computing time and avoid element inversion during the mesh deformation procedure, we introduce a coarse higher-order auxiliary mesh, which is used only to capture the structural deformation and extend it to the fluid domain. The shell structure is modeled by a FEM formulation with nodal positions and components of an unconstrained vector as degrees of freedom, which avoids the need for dealing with large rotations approximations. We solve the fluid dynamics equations in the ALE description using an implicit time marching temporal integrator and stabilized mixed FEM spatial discretization. Finally, the accuracy and robustness of the proposed method are tested with numerical examples compared to the literature results. [ABSTRACT FROM AUTHOR]

An alternative solid finite element formulation for large deformation analysis of viscoelastic materials is proposed. This new approach is based on positions and makes possible a robust implementation of an isoparametric solid tetrahedral that presents no locking when dealing with complex stress, strain and strain rate for general structural analysis. A consistent way to write internal variables that accounts for finite viscoelastic strains is proposed. In this alternative methodology the neo-Hookean hyperelastic law is taken into account together with the Zener viscoelastic model. The evolution law is described in terms of a rate equation involving the viscous right Cauchy-Green stretch tensor. The study is dedicated to homogeneous materials under isothermal and quasi-static conditions. The nonlinear solution procedure is performed via the Newton-Raphson iterative technique and the backward-Euler method. Four illustrative examples involving large viscoelastic strains are analyzed: uniaxial tension, simple shear, buckling of a clamped column and partially loaded block. The present formulation can reproduce creep, stress relaxation and viscoelastic rate dependent stiffening at large strains, which are usually observed in polymeric materials. Even for very complex stress, strain and strain rates the mesh refinement of the proposed methodology leads to more accurate results, avoiding general locking problems. The effect of the viscosity parameter on the material response and the evolution of viscous stretches over time are also highlighted in the results. [ABSTRACT FROM AUTHOR]

In this work we extend a total Lagrangian formulation developed for dynamical nonlinear analysis of elastic plane frames to include structural energy dissipation and sliding connections (as prismatic and cylindrical joints). The joints move in a path that may present an arbitrary roughness profile along its trajectory. Their exact kinematical restraints are introduced in the total mechanical energy of the system by the method of Lagrange multipliers. The structural energy dissipation is considered by a modified Kelvin-Voigt rheological model, for which a pure numerical procedure for the strain rate approximation (finite difference) is proposed. The dynamical equilibrium equation is obtained by a variational principle and the nonlinear solution procedure is done by the Newton-Raphson method. Several examples are presented to demonstrate the efficiency of the proposed formulations. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the FEM solution of laminated plates and shells that nowadays are mostly done by low order solid or shell finite elements enriched by stress or strain fields, or by specific kinematics dedicated to the analysis of such structures. We introduce a triangular based prismatic finite element of any approximation order capable of solving from very thin to very thick laminated plates and shells, with the following properties: (i) locking-free behavior; (ii) good stress distribution even for complex materials; (iii) geometrically exact description of large displacements; and (iv) geometry dedicated to evaluate plates and shells (laminated or not) free of problems due to distorted meshes or ill-conditioned systems as thickness decreases. This triangular based prismatic finite element can also be employed in laminated beams, holding the same properties. The proposed element uses total Lagrangian description based on positions, and its performance regarding the claimed properties is demonstrated in several examples. [ABSTRACT FROM AUTHOR]

Without adding new degrees of freedom, this paper presents a new finite element formulation that combines three important ingredients for precise analysis of displacements and transverse stresses in laminated shells and plates, namely: (i) Presence of Zig-Zag effect, (ii) regularization of transverse stresses in order to guaranty their continuity and (iii) cinematically exact description in FEM nonlinear geometric formulation. The accuracy of the proposed formulation in both displacements and stresses will be proven by comparing results with linear elastic benchmarks of literature. Furthermore, the possibilities of the formulation are shown by solving an extreme geometric nonlinear problem of orthotropic laminated shells, considering results in displacements and stresses. [ABSTRACT FROM AUTHOR]

This paper presents a two-dimensional frame finite element methodology to deal with flexible multi-body dynamic systems and applies it to building progressive collapse analysis. The proposed methodology employs a frame element with Timoshenko kinematics and the dynamic governing equation is solved based on the stationary potential energy theorem written regarding nodal positions and generalized vectors components instead of displacements and rotations. The bodies are discretized by lose finite elements, which are assembled by Lagrange multipliers in order to make possible dynamical detachment. Due to the absence of rotation, the time integration is carried by classical Newmark algorithm, which reveals to be stable to the position based formulation. The accuracy of the proposed formulation is verified by simple examples and its capabilities regarding progressive collapse analysis is demonstrated in a more complete building analysis. [ABSTRACT FROM AUTHOR]

In this study a total lagrangian 2D finite element formulation is used to model plane frames developing large displacements and rotations considering sliding connections. This kind of connections is usually called prismatic and cylindrical joints. In order to be self-containing, the steps of the development of a frame finite element of any approximation order that considers the influence of shear strain by means of a generalized Reissner kinematics is presented. The adopted degrees of freedom are positions and rotations. Using positions as degrees of freedom simplifies the total lagrangian description and enables a comprehensive presentation of the proposed connections. Revolute connections are considered by direct degrees of freedom matching. Prismatic connections are modelled by the Lagrange multiplier technique that constrains positions and rotation of a sliding node to the varying position and rotation of a path element. Cylindrical joints are introduced in similar way by Lagrange multipliers releasing the sliding node rotation. The principle of stationary potential energy is used to write the non-linear equilibrium equation including the Lagrange multiplier influence. To solve the non-linear equation a Taylor expansion is carried out and the Newton-Raphson procedure is employed. The frame element is considered elastic, following the Saint-Venant- Kirchhoff constitutive model. Selected examples are used to validate the formulation and to show its possibilities of application. [ABSTRACT FROM AUTHOR]

In this work we are interested to provide an alternative way to model particulate composites by the Finite Element Method. Our proposal allows the inclusion of particles with any geometry, quantity and any regular or random arrangement in continuous matrix. Accordingly, the main feature of the formulation is: maintaining the geometry and the discretization of the matrix, to introduce a given distribution of particles without increasing the number of degrees of freedom or change the initial mesh of the problem. In this sense a direct FEM approach for particulate composites arise. Here, both the matrix and particles are considered elastic and totally connected, i.e., degeneration of the involved materials is not allowed and perfect adherence between matrix and particles phases is adopted, thus the interface or the transition zone between phases is not modeled. The proposed formulation already includes geometrically exact description allowing the development of large displacements and moderate strains. Examples are presented to validate the formulation confronting it with usual techniques of homogenization and laboratory experiments. Furthermore, the possibilities of the proposed technique are shown in an original example. [ABSTRACT FROM AUTHOR]

This study proposes a new pure numerical way to model mass / spring / damper devices to control the vibration of truss structures developing large displacements. It avoids the solution of local differential equations present in traditional convolution approaches to solve viscoelasticity. The structure is modeled by the geometrically exact Finite Element Method based on positions. The introduction of the device's mass is made by means of Lagrange multipliers that imposes its movement along the straight line of a finite element. A pure numerical Kelvin/Voigt like rheological model capable of nonlinear large deformations is originally proposed here. It is numerically solved along time to accomplish the damping parameters of the device. Examples are solved to validate the formulation and to show the practical possibilities of the proposed technique. [ABSTRACT FROM AUTHOR]

In this study we present an alternative finite element formulation to solve two-dimensional laminated and functionally graded bar elements with continuum transverse stress distribution. The considered structural elements are long or short and the strain level can be large. Thus, it is necessary to consider a hyperelastic constitutive model capable of representing large strains. Enhancements - regularization of the Reissner-Mindlin kinematics and the zigzag effect - are developed to impose continuous transverse shear stress. The regularized Reissner-Mindlin kinematics is important for both laminated and functionally graded materials, while the zigzag enhancement is important only for laminates. The formulation is developed considering laminated bars; however, as the number of laminas is unlimited and keeps the number of degrees of freedom; functionally graded materials are directly represented. An additional degree of freedom is considered for large strains, improving the element volumetric performance. The formulation is validated comparing the proposed kinematics with literature results. [ABSTRACT FROM AUTHOR]

In this paper, a solid finite element formulation applied to the analysis of functionally graded materials (FGMs) under finite elastoplastic deformation with mixed hardening is presented. The main novelty of this paper is the use of gradually variable material coefficients in finite elastoplastic strain regime. The numerical simulations are performed with the same constitutive models but with different variations of the material coefficients. Full integration and high order tetrahedral elements are used. Results show that high order elements and mesh refinement avoids general locking problems. Finally, the differences (regarding final results) between the homogeneous and the FG cases are depicted. [ABSTRACT FROM AUTHOR]

In this study we apply the total Lagrangian formulation based on positions to develop a strategy for the physical and geometrical nonlinear analysis of plane structures and mechanisms. The developed frame elements have cross sections constituted by laminas of different materials and widths. The Reissner–Mindlin kinematics is adopted to include shear effects into the formulation. These elements are connected among each other by semi-rigid connections. Both elements and connections have multi-linear elastoplastic behavior with isotropic hardening. An alternative flow direction rule, which allows the reproduction of any stress–strain curve and the determination of closed solution for the plastic multiplier, is shown. All steps to reproduce the formulation are provided. Various examples are used to demonstrate the good behavior of the formulation, including a progressive collapse analysis of a tall building subjected to a real seismic load. [ABSTRACT FROM AUTHOR]

This study presents the development of a finite element formulation based on positions to deal with steel structures under high temperatures. The nonlinear thermal analysis is done regarding cross sections using two-dimensional flat elements while the three dimensional structural members are modeled by physical and geometrical nonlinear solid-like frame elements of any order. The thermal analysis consists in achieving, along time, the temperature profile at frame elements cross sections that affects the constitutive relations and, consequently, residual stresses at the structural mechanical equilibrium. The proposed element presents a geometrically exact description for large displacements and rotations by means of translations and generalized vectors nodal parameters. The adopted three dimensional Thermo-elastoplastic constitutive relation is based on the von Mises yielding surface for which the temperature dependence is established and an alternative flow rule is developed. Several examples are presented in order to validate the formulation and to show its good results. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we develop a partitioned algorithm for three-dimensional geometric non-linear fluid–structure interaction analysis using the finite element method. The fluid solver is explicit and its time integration based on characteristics, which automatically introduces stabilising terms on stream direction. The Navier–Stokes equations are written using the arbitrary Lagrangian–Eulerian (ALE) description, in order to accept moving boundaries and coupling with Lagrangian shell elements. The structure is modelled using a novel finite element method formulation for geometric non-linear shell dynamics. Such shell formulation, so-called positional formulation, is based on the minimum potential energy theorem, written regarding nodal positions and generalised unconstrained vectors, not displacements and rotations. These characteristics avoid the use of large rotation approximations. The coupling between the two different meshes is done by mapping the fluid boundary nodes local positions over the shell elements and vice versa, avoiding the need for matching fluid and shell nodes. The fluid mesh is adapted using a simple approach based on shell positions and velocities. The efficiency and robustness of the proposed approach is demonstrated by examples. [Copyright &y& Elsevier]

Abstract: In this work the finite element method (FEM) is applied to simulate orthotropic laminated plates and shells presenting large deformations. Alternatively to co-rotational and strain or stress assumed enhanced solid-like elements, a total Lagrangian technique based on unconstrained vectors and position description is proposed. As a consequence, there is no necessity to apply the linearized finite rotation formulae, as for example the Euler–Rodrigues one. The proposed laminate orthotropic strategy can be used for any order isoparametric curved elements; in this study we only explored cubic elements. Equilibrium is achieved from the principle of minimum total potential energy. Examples are solved in order to demonstrate the precision and robustness of the proposed procedure comparing results to analytical and other numerical solutions. [Copyright &y& Elsevier]

Abstract: This study presents an alternative three-dimensional geometric non-linear frame formulation based on generalized unconstrained vector and positions to solve structures and mechanisms subjected to dynamic loading. The formulation is classified as total Lagrangian with exact kinematic description. The resulting element presents warping and non-constant transverse strain modes, which guarantees locking-free behavior for the adopted three-dimensional constitutive relation, Saint-Venant–Kirchhoff, for instance. The application of generalized vectors is an alternative to the use of finite rotations and rigid triad''s formulae. Spherical and revolute joints are considered and selected dynamic and static examples are presented to demonstrate the accuracy and generality of the proposed technique. [Copyright &y& Elsevier]

Abstract: This paper presents a formulation to deal with dynamic thermomechanical problems by the finite element method. The proposed methodology is based on the minimum potential energy theorem written regarding nodal positions, not displacements, to solve the mechanical problem. The thermal problem is solved by a regular finite element method. Such formulation has the advantage of being simple and accurate. As a solution strategy, it has been used as a natural split of the thermomechanical problem, usually called isothermal split or isothermal staggered algorithm. Usual internal variables and the additive decomposition of the strain tensor have been adopted to model the plastic behavior. Four examples are presented to show the applicability of the technique. The results are compared with other authors’ numerical solutions and experimental results. [ABSTRACT FROM AUTHOR]

Abstract: The most ordinary finite element formulations for 3D frame analysis do not consider the warping of cross-sections as part of their kinematics. So the stiffness, regarding torsion, should be directly introduced by the user into the computational software and the bar is treated as it is working under no warping hypothesis. This approach does not give good results for general structural elements applied in engineering. Both displacement and stress calculation reveal sensible deficiencies for both linear and non-linear applications. For linear analysis, displacements can be corrected by assuming a stiffness that results in acceptable global displacements of the analyzed structure. However, the stress calculation will be far from reality. For nonlinear analysis the deficiencies are even worse. In the past forty years, some special structural matrix analysis and finite element formulations have been proposed in literature to include warping and the bending-torsion effects for 3D general frame analysis considering both linear and non-linear situations. In this work, using a kinematics improvement technique, the degree of freedom “warping intensity” is introduced following a new approach for 3D frame elements. This degree of freedom is associated with the warping basic mode, a geometric characteristic of the cross-section. It does not have a direct relation with the rate of twist rotation along the longitudinal axis, as in existent formulations. Moreover, a linear strain variation mode is provided for the geometric non-linear approach, for which complete 3D constitutive relation (Saint–Venant Kirchhoff) is adopted. The proposed technique allows the consideration of inhomogeneous cross-sections with any geometry. Various examples are shown to demonstrate the accuracy and applicability of the proposed formulation. [Copyright &y& Elsevier]

Abstract: This study presents a solid-like finite element formulation to solve geometric non-linear three-dimensional inhomogeneous frames. To achieve the desired representation, unconstrained vectors are used instead of the classic rigid director triad; as a consequence, the resulting formulation does not use finite rotation schemes. High order curved elements with any cross section are developed using a full three-dimensional constitutive elastic relation. Warping and variable thickness strain modes are introduced to avoid locking. The warping mode is solved numerically in FEM pre-processing computational code, which is coupled to the main program. The extra calculations are relatively small when the number of finite elements, with the same cross section, increases. The warping mode is based on a 2D free torsion (Saint–Venant) problem that considers inhomogeneous material. A scheme that automatically generates shape functions and its derivatives allow the use of any degree of approximation for the developed frame element. General examples are solved to check the objectivity, path independence, locking free behavior, generality and accuracy of the proposed formulation. [Copyright &y& Elsevier]

This paper presents a simple two dimensional frame formulation to deal with structures undergoing large motions due to dynamic actions including very thin inflatable structures, balloons. The proposed methodology is based on the minimum potential energy theorem written regarding nodal positions. Velocity, acceleration and strain are achieved directly from positions, not displacements, characterizing the novelty of the proposed technique. A non-dimensional space is created and the deformation function (change of configuration) is written following two independent mappings from which the strain energy function is written. The classical Newmark equations are used to integrate time. Dumping and non-conservative forces are introduced into the mechanical system by a rheonomic energy function. The final formulation has the advantage of being simple and easy to teach, when compared to classical counterparts. The behavior of a bench-mark problem (spin-up maneuver) is solved to prove the formulation regarding high circumferential speed applications. Other examples are dedicated to inflatable and very thin structures, in order to test the formulation for further analysis of three dimensional balloons. [ABSTRACT FROM AUTHOR]

This work presents a fully non-linear finite element formulation for shell analysis comprising linear strain variation along the thickness of the shell and geometrically exact description for curved triangular elements. The developed formulation assumes positions and generalized unconstrained vectors as the variables of the problem, not displacements and finite rotations. The full 3D Saint-Venant-Kirchhoff constitutive relation is adopted and, to avoid locking, the rate of thickness variation enhancement is introduced. As a consequence, the second Piola-Kirchhoff stress tensor and the Green strain measure are employed to derive the specific strain energy potential. Curved triangular elements with cubic approximation are adopted using simple notation. Selected numerical simulations illustrate and confirm the objectivity, accuracy, path independence and applicability of the proposed technique. [ABSTRACT FROM AUTHOR]

This work presents an alternative finite element shell formulation based on non-conventional nodal parameters. The considered parameters are nodal positions (not displacements) and generalized vector components that comprise both director cossines and shell thickness variation at the same time. Although any objective strain measure could be adopted to develop the proposed formulation, non-linear engineering strain is chosen in order to take advantage of well know linear engineering stress–strain relations and to complement the easy geometrical appeal of positional formulation. The resulting formulation presents six degrees of freedom by each node and considers constant thickness variation. Consequently, the formulation fulfills a three dimensional compatible mapping and requires a relaxed three-dimensional constitutive relation to avoid thickness locking. Curved triangular elements with cubic approximation are adopted following a very simple notation. Several numerical simulations illustrate and confirm the accuracy and applicability of the proposed formulation. [ABSTRACT FROM AUTHOR]

Abstract In this study, for the first time, we present a shell finite element based on positions and generalized vectors for instability analysis of thin-walled members. The presence of generalized vectors and transverse strain enhancement guarantee to the proposed formulation a good representation of strain and stress fields inside the element, allowing the use of complete three-dimensional constitutive law without any locking. The proposed formulation is total Lagrangian and naturally covers large displacement modeling. In past studies, the presence of generalized vectors limited the connection of shell portions or non-tangential panels, making it difficult to model thin-walled members. To solve this problem, a strategy to ensure the connection between non-coplanar elements, considering the stiffness of the connecting material, is originally developed and presented in this paper. In numerical examples we explore differences among buckling load achieved using small displacements and first limit points (or bifurcation points) using large displacements. The influence and the sensitivity of the connection stiffness are also tested when comparing these values. Results are validated against literature reference values and new examples are proposed to show the applicability of the positional formulation. Highlights • Instability analysis of thin-walled members. • Critical Load for small and large displacements. • Exact geometrical non linear structural analysis. • Enhanced high order shell elements free of locking. • New penalty connections for unconstrained vectors in shell elements. [ABSTRACT FROM AUTHOR]

In this paper, we propose an original FEM strategy to consider stiffening honeycomb-shaped cells, filled or not, to the simulation of sandwich plates and shells. The strategy combines three-dimensional membrane elements (called active face) with solid prismatic elements. This approach is different from the usual ones that use solid elements to discretize all parts of a panel or use equivalent macroscopic properties to simulate honeycomb-shape laminated composites. In the proposed technique, the composition of elements is done by means of direct nodal correspondence, defined in the mesh generation procedure, not interfering in the number of degrees of freedom of the models. Thus, introduction of reinforcements does not increase the number of degrees of freedom, which makes the technique highly economical from the numerical point of view. Positional finite element (Positional FEM) procedure is adopted, resulting in a total Lagrangian description that allows general applications including large displacements of laminated plate and shell problems. Positional FEM adopts as main variables the current nodal positions instead of displacements as classical finite elements do. The proposed stiffening cell element is tested regarding stress and displacements calculations, comparing results with literature. Results for large displacements in reinforced honeycomb laminated shells are also presented. [ABSTRACT FROM AUTHOR]

This paper reports the results of an investigation on the use of Generalised Beam Theory (GBT) to analyse the vibration behaviour of thin-walled steel frames. After an overview of the main concepts and procedures involved in performing a GBT vibration analysis, the formulation and implementation of a GBT-based beam finite element are presented, namely the determination of the finite element and frame linear stiffness and mass matrices (incorporating the influence frame joint configurations). Finally, in order to illustrate the application and capabilities of the proposed GBT-based finite element formulation, numerical results concerning the local, distortional and global vibration behaviour of (i) a symmetric portal frame and (ii) an “L-shaped” frame exhibiting four commonly used joint configurations are presented and discussed. For validation purposes, some GBT results (frequency values and vibration mode shapes) are compared with values yielded by A nsys shell finite element analyses . [ABSTRACT FROM AUTHOR]

In this work we present a generalization of a finite element formulation, based on the new Unconstrained Vector Layerwise Theory (UVLWT), that allows a geometrically exact description of 2D laminated plane frames with accurate stress distribution. The formulation presents a natural and easy extension for 3D applications. The proposed generalization is based on a penalty strategy to couple frames at corners in a very accurate and elegant way. It consists on the introduction of rigid, semi-rigid and hinged connections among elements, for which all degrees of freedom of each lamina are considered and their energetically conjugate forces calculated. Flexible supports of the structure regarding the static reference have also been successfully developed and implemented. Although two-dimensional frames are the main object of this study, three-dimensional connection expressions are developed in order to promote future developments and insights. In order to have complete solutions, even when a snap-back or snap-trough occur, we present the arc-length approach adapted to the complete analysis of 2D frames by the UVLWT. From the analyzed examples, we can state that the UVLWT formulation and the developed connections presents the following capabilities:(i) geometric nonlinear modeling of laminated 2D frames assembled by slender or thick bars, without presenting problems of locking and system of equations bad conditioning; (ii) geometrically exact modeling of curved bars; (iii) consistent modeling of general flexible or rigid internal corner connections; (iv) consistent modeling of elastic external supports; (v) Zig-Zag effect consideration with accurate transverse stress distribution and (vi) straightforward extension for 3D applications as the finite rotation concept is not used. [ABSTRACT FROM AUTHOR]

In this study, a specific formulation and its corresponding computational code are developed using: (i) an alternative 3D finite strain elastoplastic theory based on the multiplicative Flory decomposition, (ii) a node-surface contact algorithm to model sheet folding and (iii) a 3D prismatic solid-based finite element with high order approximation. Employing the developed code, a sequential analysis is presented that involves (i) folding an initially flat sheet in the dimensions of the studied thin-walled U-member, from which results the residual stresses of the manufacturing process, (ii) changing the boundary conditions to enable the application of linear basic loads that generate the buckling situation and (iii) solving the buckling of the cold-formed thin-walled U-member. We used literature benchmarks to show that the proposed 3D elastoplastic theory is sufficiently accurate to study the influence of residual stresses and geometric defects (residual deformations) – arising from the folding process – on the critical loads of the studied U-member. • Flory's decomposition applied in finite strain plasticity. • Cold-forming of thin-walled members. • Residual stresses and strains in instability analysis. • Incremental numerical procedure by the Positional FEM. [ABSTRACT FROM AUTHOR]

The analysis of laminated structures presents three major challenges that will be handled in this study: (i) Accurate determination of transverse stresses. (ii) Nonlinear geometric behavior of structural elements which are usually slender and present large displacements and rotations. (iii) Conditioning improvement of stiffness matrix that, in general, is weakened when using very thin elements. In this study, a geometrically exact nonlinear formulation based on positions is proposed to model straight and curved laminated frame elements. This formulation has similarity with the well known Layerwise Theory (LWT), however it uses positions and generalized vectors as nodal parameters instead of displacement degrees of freedom for different nodes and laminas. The proposed formulation is called Unconstrained Vector/Layerwise Theory (UVLWT). The proposed kinematics eliminates the ill conditioning of stiffness matrix for thin elements, as the positions of any point of the continuum are tied to nodal positions. The Saint–Venant–Kirchhoff constitutive law is adopted to describe geometrical nonlinearity. The developed formulation is total Lagrangian and the considered degrees of freedom are positions and laminated cross sections generalized vectors. Results for various straight and curved elements with different height/length ratios are used to demonstrate the capabilities of the proposed formulation. [ABSTRACT FROM AUTHOR]

This study intends to contribute with the improvement of FEM formulations to analyze composite materials and structures at the meso and macro levels. Specifically, composite materials and structures constituted by an elastic matrix reinforced by long or short fibers that may debound when the contact stress reaches a critical value are taken into account. The study proposes a way to introduce fibers (short or long) inside elastic solids modeled by finite elements without increasing the number of degrees of freedom when debounding is not present. When there is debounding, new degrees of freedom are incorporated only at the slipping contact between fibers and matrix following an elastoplastic non-linear constitutive relation. The matrix is considered elastic while fibers follow a multi-linear elastoplastic constitutive relation. Large deformations and moderate strains are considered. In order to model the debounding between fibers and matrix it is necessary to accurately calculate the contact stresses. Therefore, the development of straight and curved fiber elements of any order and the accuracy analysis of the proposed contact stress calculations are investigated. After defining the best strategy to be followed general examples are solved to validate the contact stress calculation, debounding and plastic fiber behavior. [ABSTRACT FROM AUTHOR]

• Shell-based thin-walled structures modeling with semi-rigid connections. • Generalized joints modeled by simple bracing panels. • Box FE for automatic slabs × beams × columns connections. • Buckling loads and critical points analysis. • Instability and geometrical nonlinear path-following analysis. In this study, we develop and propose a finite element (Box Element) designed specially to improve the shell-based simulation of elastic thin-walled structures. The Box Element (BE) allows a simple and automatic connection between beams and columns, as well as, between slabs and beams. The BE stiffness is assembled by bracing panels immersed in its numerical structure simulating the flexibility of connections. Its formulation is developed using an in house positional FEM code, whose 3D rotation degrees of freedom are replaced by generalized vectors, facilitating bending couplings and large rotation modeling. Instability and geometrical nonlinear path-following analysis are studied in examples, comparing results with literature benchmarks and proposing a practical application. [ABSTRACT FROM AUTHOR]

• Sandwich composite plates and shells. • Active face prismatic FE based on positions. • Core stiffening honeycomb cell. • Exact geometrical nonlinear analysis. • Displacement and stress calculations. • Natural Frequencies of Honeycomb sandwich plates. In this paper a strategy for the stress analysis of sandwich plates and shells employing the active face triangular-based prismatic finite element is provided, which combines three-dimensional membrane elements (called active face) with solid elements providing stiffening cells, usually called honeycomb. The connection of solid and active face elements is done by direct nodal correspondence, keeping the total number of degrees of freedom unaltered, which makes the technique highly economical from the numerical point of view. Orthotropic properties are specially addressed, which are important for material failure criteria studies. The accuracy of the active face prismatic finite element is also evaluated in the calculation of natural frequencies of honeycomb sandwich panels for acoustic vibration isolation purposes, for instance. Results for orthotropic sandwich plates and shells are presented and compared with established commercial software and literature results. [ABSTRACT FROM AUTHOR]