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 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 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.