# FEM Analyses

The aim of structural analysis is to predict the level of stresses and deformations of an object depending on its material properties, load type and the way it is fixed. That enables determination if the design is strong enough to support the designed loads or if the material is used economically.

Owing to their geometrical complexity, most of the structures need to be analyzed using specific computer programs and numerical. The most common approach is the so-called finite element method, FEM. The object of our interest is divided into multiple simpler objects (these are the finite elements). Their mechanical interactions are the subject of our calculations and are found in an approximate manner using specialized computational model.

## Benefits of an FEM structural analysis:

- prediction of critical areas in the project, including stress concentration zones,

- minimization of the material use and cost,

- shape optimization of the structure so that internal loads are minimized.

## Types of FEM consulting services offered by QuickerSim:

- linear static analyses

- heat-dependent loads

- non-linear analyses (large deformations, contact, plasticity)

- analysis coupled with fluid flow (so-called Fluid-Structure Interaction, FSI)

- optimization analyses, recommending geometric modifications

We offer the analyses as stand-alone consultancy services as well as perform them in comprehensive projects.

## What software do we use for structural analyses?

We use both commercial software (Dassault Systems SolidWorks, MATLAB) as well as the well-established open-source solutions (GMSH for mesh generation, Paraview for post-processing). For non-standard cases, we write our own computational modules and scripts usually using MATLAB.

In the case of the optimization problems, we resort to a series of specific methods such as gradient-based algorithms, adjoint equations or dedicated optimization packages (MATLAB Optimization Toolbox of NLOpt).

## How is the FEM analysis carried out?

The FEM analysis is all about performing the strength calculations based on the so-called discrete computer model of the structure. It consists of a few distinct steps. First, based on the CAD geometry model the computational grid (called the mesh) is generated. The colles of this mesh constitute the finite elements. After mesh generation, the boundary conditions are applied. They describe the way the structure is bound (revolute joints, stiff connections, loose ends,)  as well as other constraints (contact, maximal deflections). After this process, the specific loads and stresses are defined: points and magnitudes of applied forces, mass-density loads (weight, inertia, centrifugal forces).

Such a numerical model is handled by the structural solver. It is a dedicated program that solves the complicated algebraic system of FEM equations and yields the results in the form of stresses, displacements as well as other fields if needed (strain, temperature, material properties). These results are judged in the post-processing module.

In the case of the optimization projects, some of these tasks have to be carried out many times. Sometimes the modification of the geometry is required so that stresses are decreased or distributed more uniformly. Depending on the problem’s complexity, these tasks can be carried out by an experienced engineer or in an automatic fashion. In the latter case, we employ dedicated algorithms based on gradient methods or adjoint equations, for example.

## USER STORY

The Polish Air-Force Research Institute ordered design of a gas micro-turbine at QuickerSim. Apart from CFD simulations, QuickerSim had to perform the strength analysis of the proposed design.

These were critical because of the large centrifugal forces – the turbine was supposed to revolve at several tens of thousands rev./min. The most loaded part of the design was the junction between the internal ring and the turbine blades. Especially the slim trailing-edge experienced a large stress-concentration factor.

Two actions were recommended. On one hand, the entire junction was rounded while on the other, the aft part was cut-off. However, because of a relatively small space between the inner and outer rings, every contraction of the flow space resulted in some deterioration of the turbine’s performance. Thus the rounding’s radius had to be minimized. Only a detailed FEM analysis could point to the exact dimension.;

 Pic. 1 Stress concentration at the trailing edge-inner ring junction Pic. 2 Undercut and rounded connection of the turbine blade and the inner ring – front and back views