# Analysis and mechanical and thermal simulations

## Introduction

In order to save costs, avoid the delays and provide a design that meets the requirements of the project “first time”, we recommend using of imaging (simulation) of the system performance and sensitivity analysis of its parameters. Perform of those analysis have many advantages:

- Early feasibility study and design concept
- Improving the design and optimization (weight loss, etc.)
- Getting answers to issues at the early stage of development and reaching the prototype stage in minimal time
- Detection of possible points of failure and the costs involved
- Savings trials, development and production costs, etc.

Lavi Engineering offers these analysis using finite element software.

## What is the method of finite elements?

Finite element method (Finite Element Analysis or FEA) is a numerical method for approximate solution of problems in all areas of engineering fields (fields efforts, heat flow, etc.) using differential equations.

This method is based on dividing the body into small discrete parts and the calculation of forces distribution in those ‘small’ parts. The term “finite element” distinguishes the differential equations mathematical method, where the elements are infinite. The method was invented in the forties of the twentieth century in the context of solving problems in buildings and vibration, and became practical solution of engineering problems in the mid-seventies, after the development of other mathematical tools and adequate computing power.

Practical use of this method is in aircraft industry, marine industry, power plants the automotive industry. The element shape is usually a cube or a pyramid – three-dimensional objects, or triangles and squares – bi-dimensional bodies. Points of contact between the elements are called nodes and are located along the edges of the element. In this way the entire body is divided into a grid of elements (mesh). Networking process and selecting type and size of the elements requires experience and knowledge. In principle, the accuracy of the solution improves with smaller elements or when used in higher-order element, namely multi-element nodes. Speed and accuracy are also affected by the elements uniformity. Software solution is performed by several algebraic techniques to the problem.

Finite element calculation is divided into two main categories: static analysis (implicit) which is characterized by relatively small movements, and dynamic analyzes (explicit) that is defined by large movements and deformations such as vehicle collisions, explosions, etc..

In solving structural problems implicit solution is performed, for example, Stiffness equation describing the relationship between forces applied and the floaters that are created as a response. Stiffness equation looks like this:

{F} = [K] * {X}

When:

{F} – the vector of forces.

{X} – vector of movement.

[K] – stiffness matrix

Significant dynamical problems (time dependent) solution process is performed equations of motion.

## System benefits

Finite element method has clear advantages over other numerical methods:

- There are no limitations of the geometry and structure of system can be of any geometric shape
- Same calculation model as for real engineering structure
- Environmental conditions are not limited and can be of any type (full or partial load, internal or external as well as integrated environmental conditions such as pressure and temperature)
- No limit for anisotropic material properties. Any material can have a non-linear anisotropic properties
- Model parts can be combined of different functional character – beams, pallets, cable, friction elements, etc.

Another very important advantage is that, you can view a simulation of the problem in the form of animation with which you can analyze the behavior of the model. Such option may not exist during the experiment, especially in processes occurring in a very short time such as changes in temperature, impact or explosion.

## Types of analyzes performed:

- Structural analysis and calculations of strength of mechanical systems (including thin films)
- Calculations of movements, stresses and collisions of a mechanical shock (dropping, launching, etc.)
- Dynamic analysis to calculate the resonance of the body
- Shivering and spectral analysis
- Steady state thermal analysis and transition state (transient)
- Simulations of thermal stresses
- Penetration of a rigid body to another hard body
- MOTION systems simulations
- Piezoelectric systems simulation

## Industries that use analysis

System analysis covers all types of industries, especially in projects where the level of safety or security factors are important. Analysis is recommended in cases where system optimization is required, design that combines heat propagation and vibration durability, in situations where product strength is critical and in cases of product failure, in order to determine the cause of the failure and fix the problem.

Electronics industries: packaging strength, heat dissipation in electronic power cards, card’s vibration, structural strength and so on.

Defense industries: meeting the specifications of military standards (mill spec), Design of integrated analyzes to minimize parts sizes, standing launch shocks, dropping, vibration of airborne parts, thermal stresses (transition from cryogenic to very high temperatures), calculation of temporary heating and cooling, evaluation of heat capacity, failures analysis.

In the automotive industry: vibration, temperature and strength analysis, resonance and component testing in real environment simulation.