We discuss a solution algorithm for quasi-static elastoplastic problems with hardening. Such problems can be described by a time dependent variational inequality, where the displacement and the plastic strain fields serve as primal variables. After discretization in time, one variational inequality of the second kind is obtained per time step and can be reformulated as each one minimization problem with a convex energy functional which depends smoothly on the displacement and non-smoothly on the plastic strain. There exists an explicit formula how to minimize the energy functional with respect to the plastic strain for a given displacement. By substitution, the energy functional can be written as a functional depending only on the displacement. The theorem of Moreau from convex analysis states that the energy functional is differentiable with an explicitly computable first derivative. The second derivative of the energy functional does not exist, hence the plastic strain minimizer is not differentiable on the elastoplastic interface, which separates the continuum in elastically and plastically deformed parts. A Newton-like method exploiting slanting functions of the energy functional's first derivative instead of the nonexistent second derivative is applied. Such method is called a slant Newton method for short. The local super-linear convergence of the slant Newton method in the discrete case is shown and sufficient regularity assumptions are formulated, which would guarantee the local super-linear convergence also in the continuous case.

No abstract

In the present paper, a three-dimensional shear deformable beam finite element is presented, which is based on the absolute nodal coordinate formulation (ANCF). The orientation of the beam’s cross section is parameterized by means of slope vectors. Both a structural mechanics based formulation of the elastic forces based on Reissner’s nonlinear rod theory, as well as a continuum mechanics based formulation for a St. Venant Kirchhoff material are presented in this paper. The performance of the proposed finite beam element is investigated by the analysis of several static and linearized dynamic problems. A comparison to results provided in the literature, to analytical solutions, and to the solution found by commercial finite element software shows high accuracy and high order of convergence, and therefore the present element has high potential for geometrically nonlinear problems.

We consider finite deformations and bending of an elastic plate moving across a given domain. Velocities of the plate are kinematically prescribed at two parallel lines, which bound the region in the direction of motion. Inhomogeneity of the velocity profile at the exit from the domain results in planar deformations and out-of-plane buckling of the plate. The presented quasistatic analysis features a novel kinematic description, in which the coordinate in the direction of motion is a Eulerian one, while the displacements in transverse and the out-of-plane directions are modeled in a Lagrangian framework. The material volume is traveling across a finite element mesh, which is aligned to the boundaries of the domain. A concise mathematical formulation results in a robust numerical scheme without the need to solve the advection (transport) equation at each time step. The model is validated against solutions of a benchmark problem with a conventional Lagrangian finite element scheme. The approach is further demonstrated by modeling the time evolution of deformation of a moving plate.

The multibody dynamics and finite element simulation code has been developed since 1997. In the past years, more than 10 researchers have contributed to certain parts of HOTINT, such as solver, graphical user interface, element library, joint library, finite element functionality and port blocks. Currently, a script-language based version of HOTINT is freely available for download, intended for research, education and industrial applications. The main features of the current available version include objects like point mass, rigid bodies, complex point-based joints, classical mechanical joints, flexible (nonlinear) beams, port-blocks for mechatronics applications and many other features such as loads, sensors and graphical objects. HOTINT includes a 3D graphical visualization showing the results immediately during simulation, which helps to reduce modelling errors. In the present paper, we show the current state and the structure of the code. Examples should demonstrate the easiness of use of HOTINT.