### FEM Simulation - The Introduction

1. Introduction FEM simulation
2. Scheme/ calculation procedure FEM
2.1. Pre-Processing
2.2. Solver
2.3. Post-Processing
3. Introduction of optimization methods
3.1 Optimization methods at Sinotec
3.1.1 Topology optimization
3.1.2 Parameter optimization ##### 1. Introduction The Finite Element Method

The finite element method is a numerical calculation method that is indispensable in product development today. The basic idea of FEM is to break down the structures to be investigated into simple subareas, the so-called finite elements, in order to then describe structural-mechanical problems such as deformations, stresses, accelerations, etc. using differential equations. The decomposition of the constructions into simple subareas (finite elements) is also called Discretization.

The finite elements can be simple one-dimensional beam elements, in the two-dimensional area triangular and quadrangular elements and in the three-dimensional area tetrahedron, pentahedron, pyramid and hexahedron elements.

The engineer's challenge in applying FEM is first of all to generate a high-quality mesh, suitable for the respective load, which provides realistic results and at the same time saves unnecessary computing time. This is because the finer a component is meshed, the longer the computing times, which is reflected in its efficiency and economy. The coarser a component is meshed, the less accurate the results become. Therefore, the goal here is to achieve a good compromise between accuracy and computing time. A further challenge for the engineer is to evaluate the results of a FE calculation (post-processing). For the correct evaluation of the beautiful colourful pictures, the calculation engineer needs not only experience and knowledge of mathematics and physics, but also knowledge of mechanics, strength, materials and design.

##### 2. In principle, every FE calculation runs according to the same scheme:
###### 2.1. Pre-Processing

a) As a rule, geometry is already available in CAD format
b) Geometry preparation/repair
c) Creation of a computable model (discretization/meshing)
d) Definition of boundary conditions (loads, mounting etc)
e) Material-Definition

###### 2.2. Solver

The stiffness matrices created from the first step, depending on the problem, mass and damping matrices, are now solved numerically by a selected solver in the second step.

###### 2.3. Post-Processing

The third and last step is the evaluation of the results generated in the second step. Due to a large number of result values, which depend on the number of elements in the model, tabular evaluations are often cumbersome. Therefore graphical evaluations using colored plots ("nice colored pictures") are very popular.

##### 3. Optimization methods

In colloquial language, the term optimization is used to describe the process of achieving the best possible result for a given situation under given conditions.

In engineering practice, concrete optimization goals are always defined for all optimization methods, which are minimized or maximized by means of specific optimization approaches. The parameters that are changed during an optimization are also called design variables.

###### 3.1.1 Topologieoptimierung

Have a decisive influence on structural behaviour. The basic aim of this optimization method is to find an ideal material distribution within a defined area ("design space") for power transmissions.

###### 3.1.2 Parameter optimization

The goal of parameter optimization is to find ideal parameters ("design variables") of any kind. Therefore, this is also the most comprehensive method in numerical optimization. Strictly speaking, topology optimization is a subset of parameter optimization.

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