Bo Torstenfelt

Contact problems with friction in general purpose finite element computer programs

Abstract A combined incremental and iterative procedure for analysis of elastostatic contact problem is presented. The method suggested may with rather small efforts be implemented in any general purpose finite element computer program. Most of the routines required by the method do already exist in a general finite element routine library. Examples of modules required are multilevelled substructuring, structural stiffness matrix assembly routines and a solver for symmetric system matrices. A wide class of ordinary elements can be used in the discretization of the the contact surfaces. Only translational freedoms are treated as unknowns in the iterative procedure. The accuracy and efficiency of the method has been verified in several applications as for example three-dimensional roller bearing calculations and shear loaded bolted joints.

Topology optimization of flow networks

The field of topology optimization is well developed for load carrying trusses, but so far not for other similar network problems. The present paper is a first study in the direction of topology op ...

An automatic incrementation technique for contact problems with friction

Abstract A numerical method for analysis of elastostatic contact problems with friction has been developed. This class of problems are load history dependent because of the irreversible nature of frictional forces. An automatic incrementation technique of the applied load has been developed and implemented in the algorithm. The method is a direct method based on an iterative procedure applied to a set of linear equations established with the finite element method. The size of the applied load increments, automatically chosen by the algorithm, is in general influenced both by the nature of the problem and of the discretization of the bodies involved. The frictional forces occurring in the slip zone of the contact area are treated as known tangential forces calculated from the normal forces in the previous iteration. This piecewise linear treatment of the frictional contact problem requires an innermost iteration loop over the applied tangential force. The tangential force must coincide with the coefficient of friction times the normal force obtained in the last iteration, otherwise a new tangential force has to be calculated and the system of equations must be solved for a new right hand side vector. The automatic incrementation technique is based on the fact that each iteration is a linear problem. A tentative load increment is used in the solution of a certain iteration. A linear scaling of this solution is performed afterwards. A load scale factor is calculated in each contact node pair where a change of contact condition will occur. The change in contact status corresponding to the node pair with the smallest load scale factor is the only change which is accomplished in a certain iteration. The uniqueness of this kind of contact problem with friction has not been mathematically proven for a general case. The method has been applied to a case of loading and unloading of an elastic halfspace by a rigid cylindrical stamp and compared to solutions by Spence and Turner.

A computational methodology for shape optimization of structures in frictionless contact

This paper presents a computational methodology for shape optimization of structures in frictionless contact, which provides a basis for developing user-friendly and efficient shape optimization software. For evaluation it has been implemented as a subsystem of a general finite element software. The overall design and main principles of operation of this software are outlined. The parts connected to shape optimization are described in more detail. The key building blocks are: analytic sensitivity analysis, an adaptive finite element method, an accurate contact solver, and a sequential convex programing optimization algorithm. Results for three model application examples are presented, in which the contact pressure and the effective stress are optimized.

Load Distribution in Flexibly Supported Three-Row Roller Slew Bearings

In general, slew bearings are less firmly supported by their mounting structures than small bearings. Hence, the load distribution around the bearing may be vastly different than that predicted by classic bearing formulas. The finite element method has been employed to determine load distribution in a three-row roller slew bearing mounted between two flexible, ring shaped supporting structures composed of beam elements. A special bar element modeling the system of two opposite rollers in contact with its raceways has been elaborated. The influence of the nonlinear force displacement characteristics of each of the rollers, as well as the influence of gaps between the rollers and its raceways have been taken into account. The nonlinear contact problem has been solved utilizing the Newton-Raphson method with continually updated stiffness matrix due to both element nonlinearity and contact status. The effect of a number of design parameters on the load distribution has been investigated.

An Evolution-Based High-Cycle Fatigue Constraint in Topology Optimization

We develop a topology optimization method including high-cycle fatigue as a constraint. The fatigue model is based on a continuous-time approach, which uses the concept of a moving endurance surface as a function of the stress history and back stress evolution. The development of damage only occurs when the stress state lies outside the endurance surface. Furthermore, an aggregation function, which approximates the maximum fatigue damage, is implemented. As the optimization workflow is sensitivity-based, the fatigue sensitivities are determined using an adjoint sensitivity analysis. The capabilities of the presented approach are tested on numerical models where the problem is to maximize the stiffness subject to high-cycle fatigue constraints.

Optimizing Thermal Barrier Coating Design Using Structural Optimization Methods

Thermal barrier coatings (TBCs) are used in gas turbines to reduce creep, thermo-mechanical fatigue, and oxidation, or to allow for reduced air cooling. TBCs may fail due to fatigue. Structural opt ...

Pressure distribution in crowned roller contacts

The fatigue life of a roller bearing is heavily influenced by the crowning profile of the rollers. The pressure distribution for different types of crowning has been studied. For solving this three-dimensional contact problem a numerical procedure for analysis of general elasto-static contact problems has been used. The method is based on an incremental and iterative algorithm applied to a set of linear equations established with finite element technique. The contact surfaces are assumed to be perfectly smooth, dry and frictionless. The pressure distribution between the bodies has been compared with results obtained from other methods. The influence on the pressure distribution by the free boundary at the end of the finite cylinders has also been investigated. It is also shown that it is possible to use the same finite element model to study different types of crowning, thus making it efficient to perform paramater surveys. A method of obtaining required or ‘optimal’ pressure distribution is suggested.