Resumo A degradação mecânica de estruturas de concreto é um fenômeno dependente da heterogeneidade do material observada em mesoescala. Como a degradação mecânica é um fenômeno localizado, elementos estruturais e estruturas podem ser simulados usando a técnica de análise multiescala concorrente. Assim, apenas as regiões mais críticas são modeladas em mesoescala, reduzindo o custo computacional em comparação com a simulação de toda a estrutura nessa escala. Este trabalho apresenta duas contribuições para a estratégia de análise multiescala concorrente. A primeira contribuição apresenta uma representação alternativa da zona de transição interfacial da mesoescala (ITZ) do concreto juntamente com uma estratégia que permite modelar partículas (agregados graúdos) sem graus de liberdade. A representação da ITZ resultante permite a modelagem de fissuras discretas mais realistas na simulação de concreto. A segunda contribuição usa elementos semelhantes a agregados sem graus de liberdade como elementos de acoplamento para modelar malhas não conformes entre diferentes meios. A técnica de acoplamento proposta não adiciona graus de liberdade e não utiliza métodos de penalização ou multiplicadores de Lagrange. Resultados experimentais e numéricos são usados para validar a formulação multiescala proposta aplicada em simulações de amostras de concreto. localizado concorrente Assim escala (ITZ graúdos meios Lagrange

Abstract The mechanical degradation of concrete structures is a phenomenon dependent on the material heterogeneity observed at mesoscale. As the mechanical degradation is a localized phenomenon, structural members and structures may be simulated using the concurrent multiscale analysis technique. Thus, only the most critical regions are modeled in mesoscale, reducing the computational cost compared to the simulation of the entire structure at this scale. This work presents two contributions in concurrent multiscale analysis. The first contribution introduces an alternative representation of the mesoscale interfacial transition zone (ITZ) of the concrete together with a strategy that allows modeling particles (coarse aggregates) without degrees of freedom. The resulting ITZ representation allows the simulation of more realistic discrete cracks in concrete modeling. The second contribution uses particle-like elements without degrees of freedom as coupling elements to model non-matching meshes between different media. The proposed coupling technique does not add degrees of freedom and does not use penalty or Lagrange Multipliers methods. Experimental and numerical results are used in order to validate the proposed multiscale formulation regarding concrete specimen simulations. Thus scale (ITZ coarse aggregates particlelike particle like nonmatching non matching media methods simulations

Abstract Friction is an important source of dissipation in dynamical systems. Properly considering it in the numerical model is fundamental to obtain stable and representative responses in structures and mechanisms. This is especially significant for the well-known Coulomb model due to discontinuity in force when stick-slip transition occurs. In this work an improved friction force model is proposed to smooth the force transition at null velocity, with an additional parameter obtained from the own system state. The improved model is employed in sliding connections of plane frames finite elements. A total Lagrangian Finite Element Method (FEM) formulation based on a positional description of the motion is employed. Using a variational principle, frictional dissipation is added to the total mechanical energy to develop the equations of motion. The resulting nonlinear equations are solved by the Newton-Raphson method accounting for the friction force update in the iterative process. Examples are presented to show the formulation effectiveness and possibilities in simulating dynamical systems that present the stick-slip effect. mechanisms wellknown well known stickslip stick slip occurs velocity state elements FEM (FEM principle NewtonRaphson Newton Raphson process effect

Abstract The fundamental difference in the solution of solids and fluids relies on the respective constitutive laws. Based on the Rivlin-Saunders-Düster-Hartmann hyperelastic model and using the Flory’s strain decomposition, we present a new total Lagrangian viscoelastic constitutive model for both Kelvin-Voigt viscoelastic solids and free-surface compressive viscous isothermal fluids. A dissipative viscous virtual work is written as a function of the time rate of isochoric invariants and its relation with the viscous stress is derived. Local time derivatives are solved by backward finite difference, allowing a consistent tangent viscoelastic constitutive tensor. The virtual work principle is used to write the weak equilibrium equation and its position-based finite element counterpart. Dynamic time integration is carried out by the Newmark β method and the Newton-Raphson procedure is used to solve time steps. The formulation is validated against experimental and numerical literature results revealing good precision. Additional examples are shown in order to demonstrate the applicability and future possibilities of the technique.

Abstract Sliding connections are present in several applications on the mechanics, civil and aerospace industries. A framework consisting on an accurate and stable formulation to describe the dynamics of flexible systems with sliding connections is developed. The total Lagrangian positional approach of the Finite Element Method is employed using 2D solid and frame elements to discretize bodies and connections. This allows a wide range of applications, particularly the local modelling of joints. The proposed formulation includes roughness along sliding paths independent from the finite element geometry discretization. Following variational principles, Lagrange multipliers are used to impose sliding constraints on the equations of motion. A direct time integration is performed by the generalized-α method and its stability in the present finite deformation context is evaluated. The resulting nonlinear equations are solved by the Newton-Raphson method. Examples are presented where the proposed framework is evaluated regarding its dynamical behavior and to solve practical scenarios for which sliding modelling is a necessity.

Abstract The importance of knowing critical loads and post-critical behavior of thin-walled structures motivates the development of several scientific and practical studies. Most references are concerned with stability analysis for small displacements (first order approach), or with second order stability analyzes, a less precise geometric nonlinear strategy. However, very flexible structures or ones that present small loss of stiffness after the first critical load need more careful analysis. Here we present a shell numerical formulation capable of carrying out stability analysis of thin-walled structures developing large displacements. This formulation uses generalized unconstrained vectors as nodal parameters instead of rotations. To make possible a complete stability analysis using unconstrained vectors, we present an original strategy that imposes a Conjugate Modal Force at the vicinity of critical points, allowing an accurate choice of post-critical paths. Non-conservative forces are also considered and results are compared with literature benchmarks, demonstrating the accuracy and capacity of the proposed formulation.

Abstract An alternative elastoplastic model based on the Flory’s right Cauchy-Green stretch tensor decomposition is proposed and applied to model soft cores of sandwich panels. It does not follow usual methodologies as the additive decomposition or the Kröner-Lee multiplicative decomposition of strains. It is based on an important hyperelastic relation, Flory’s decomposition, from which the total strain is separated in two isochoric and one volumetric parts. Using this decomposition, the volumetric strain energy continues to be elastic during all elastoplastic analysis and the isochoric parts are managed to produce the plastic evolution. As a consequence of Flory’s decomposition, the plastic flow direction is known and independent of the yielding surfaces. Moreover, it provides the well known deviatoric nature of plastic strains. For validation purposes, the resulting formulation is implemented using a special 3D prismatic element in a geometrical nonlinear positional FEM computational code. The achieved numerical results are compared with literature experimental data of soft core laminated structural elements.

Abstract An alternative geometrically nonlinear total Lagrangian finite element is presented and applied to solve cable, cable nets and a very long suspended bridge in both three and two-dimensional spaces from its setting-up through its response to earthquake. It includes dynamics, pseudo-dynamics regularization, elastic actuators and automatic stress calibration. Dynamics and pseudo-dynamics are used to perform transient structural analysis and the setting-up of very unstable structures. Elastic actuators allow pre-stressing structural members for the iterative structural design and cables natural length definition. Automatic stress calibration comprises continuous cables in complicated structures without sliding contact devices. The formulation is applied to model main cables of suspended bridges passing through saddle points. Inertial terms are introduced by an alternative mathematical way. Two simple examples are used to validate all aspects of the proposed formulation. Finally, a representative application is performed, i.e., the numerical design and analysis of a very long span suspension bridge by the proposed strategy.

Abstract 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 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 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

AbstractThis paper presents a finite element formulation for the analysis of two dimensional reinforced elastic solids developing both small and large deformations without increasing the number of degrees of freedom. Fibers are spread inside the domain without the necessity of node coincidence. Contact stress analysis is carried out for both straight and curved elements via two different strategies. The first employs consistent differential relations and the second adopts a simple average calculation. The development of all equations is described along the paper. Numerical examples are employed to demonstrate the behavior of the proposed methodology and to compare the contact stress results for both calculations.

This study presents an alternative Finite Element formulation based on positions to model plane frames considering geometrical non-linear and elastoplastic behavior for members and semi-rigid connections. The formulation includes shear effects and allows the consideration of important mechanical behavior of structures in design decisions and verifications. The principle of stationary energy is used to find the equilibrium equations. A multi-linear elastoplastic constitutive law is developed for both continuum members and semi-rigid connections in order to comprise any proposed stress-strain diagram. Large rotations and displacements are considered for both semi-rigid connections and structure. The most important steps used to derive the formulation are described along the paper and various examples are used to validate and show the possibilities of the proposed technique.

In this work it is presented a coupling between the Boundary Element Method (BEM) and the Finite Element Method (FEM) for two-dimensional elastostatic analysis of frame-solid interaction. The BEM is used to model the matrix while the reinforcement is modeled by the FEM. Regarding the coupling formulation a third degree polynomial is adopted to describe the displacement and rotations of the reinforcement, while a linear polynomial is used to describe the contact force among the domain (matrix) and the reinforcement. Perfect bounding contact forces are improved by means of redundant equations and Least squares method. Slip-bounding with two and three paths written as function of relative displacement are used to calculate the transmitted contact forces. Examples are used to demonstrate that the proposed slip-bounding procedure regularizes the contact force behavior.

This paper presents an alternative coupling strategy between the Boundary Element Method (BEM) and the Finite Element Method (FEM) in order to create a computational code for the analysis of geometrical nonlinear 2D frames coupled to layered soils. The soil is modeled via BEM, considering multiple inclusions and internal load lines, through an alternative formulation to eliminate traction variables on subregions interfaces. A total Lagrangean formulation based on positions is adopted for the consideration of the geometric nonlinear behavior of frame structures with exact kinematics. The numerical coupling is performed by an algebraic strategy that extracts and condenses the equivalent soil's stiffness matrix and contact forces to be introduced into the frame structures hessian matrix and internal force vector, respectively. The formulation covers the analysis of shallow foundation structures and piles in any direction. Furthermore, the piles can pass through different layers. Numerical examples are shown in order to illustrate and confirm the accuracy and applicability of the proposed technique.

In this article a two-dimensional transient boundary element formulation based on the mass matrix approach is discussed. The implicit formulation of the method to deal with elastoplastic analysis is considered, as well as the way to deal with viscous damping effects. The time integration processes are based on the Newmark rhoand Houbolt methods, while the domain integrals for mass, elastoplastic and damping effects are carried out by the well known cell approximation technique. The boundary element algebraic relations are also coupled with finite element frame relations to solve stiffened domains. Some examples to illustrate the accuracy and efficiency of the proposed formulation are also presented.