# FEM calculations

In many cases a component und load complexity is available which can not be solved with analytical calculation methods. The finite element method (FEM) is a numerical calculation method to solve such general field problems like e.g. heat radiation and heat conduction, flow processes and stress analysis. For this purpose the complex continuum is separated in finite subareas, that means “finite elements” and the solution is than determined for these single areas in consideration of all global boundary conditions.

In relation to the nuclear verification the finite element method is used predominantly in strength calculations as well as in simulation of flow processes and general thermal processes. More than two decades calculation experience in this field result in a large know how in solving different problems. In dependence of the problem statements we develop individual concepts and proofs in consideration of the valid technical guideline.

For the procedure of structural-mechanical considerations the commercial FE program system ANSYS is used by the KAE GmbH. The components and structures respectively which are investigated are thereby always modelled three-dimensional because only in this way an exact evaluation of the real situation is given. Beside simple static linear-elastic strength analysis nowadays – thanks to powerful PC-systems – predominantly dynamic analysis with elastic-plastic material behaviour under temperature influence are carried out.

## 1. Strength calculations

The subsequent example shows the force transmission of a clamp on a pipe and cam respectively. Beside the outer mechanical load of the clamp the simulation result is determined especially from the image quality of the contact problem clamp/pipe.

In the next example the plastic deformation of a pipe wall beneath a dynamical load – in this case the striking of a quickly moving body - is calculated.

The third example shows the deformation of a vent stack beneath wind flow. Beside the global behaviour of the vent stack tube here especially the internal deformation of the tube is calculated which can lead to immense loads of the tube bracing.

## 2. Modal calculations

For the determination and evaluation of dynamical behaviour of components and structures firstly a modal analysis is carried out, that means the calculation of eigenfrequencies and eigenmodes. Together with the specific damping parameters quantitative statements about the vibration behaviour of the components beneath dynamical loads, e.g. earthquake, can be made.

## 3. Fatigue analysis

The fatigue of materials and components is an important and security-relevant theme for cyclic, mechanic and thermic loads and therefore a fundamental part of a serious ageing management. Only with a fatigue analysis the fatigue strength and operational stability can be shown and proven. Thus the failure of the component due to fatigue can be excluded.

In the subsequent example the calculation results (degree of fatigue) of the detailed method of "general elastic-plastic fatigue analysis" according to KTA 3201.2 are compared and evaluated with results of other less detailed methods of fatigue analysis according to KTA 3201.2 and FAMOS-level 3 respectively.

Example: fatigue of a pressurizer fitting

## 4. Fracture mechanical analysis

Fracture mechanical analysis can be made in two different ways. The first method based on the analysis of the stress state in the undisturbed component, which means without crack, by classical FE-analysis like under “strength calculations” described. By downstream, mostly empirical analytical methods a critical crack size in dependence of the prevailing stress state can be determined.

A significantly exacter method of the evaluation of existing and postulated cracks respectively is the determination of fracture mechanical parameters like e.g. stress intensity factor and T-stresses. Furthermore with these values a serious statement about the crack propagation and the remaining lifetime respectively of a component beneath certain loads is possible.

Example: crack growth