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# The FEM Method Applied to Thermal Bridges

Discover how to calculate thermal bridges using the Finite Element Method (FEM) and maximize building energy efficiency

The use of Finite Element Method (FEM) simulation proves to be a valuable tool for technicians, allowing for detailed analysis and better building design. This aims to reduce various factors influencing energy consumption, including thermal bridges that play a significant role, leading to heat losses resulting in inefficiency and higher management costs.

In this article, we will explore what the Finite Element Method is and how it can be utilized to identify and eliminate thermal bridges, aided by a software for thermal bridge calculation.

Use of FEM methodology for thermal bridge calculation

## What are Thermal Bridges

Thermal bridges are areas within a building where heat is lost between indoor and outdoor environments due to various situations, such as interruptions in insulation continuity, the presence of conductive structural elements, or the formation of cold spots due to building geometry. Their presence can lead to increased energy consumption for heating or cooling indoor spaces and greater discomfort for building occupants.

## What is the FEM Methodology

The Finite Element Method (FEM) is an advanced numerical analysis technique used in engineering to solve complex partial differential equations describing the behavior of a physical system. This innovative approach subdivides the object or structure into a large number of simpler finite elements, such as triangles or quadrilaterals in 2D and tetrahedra in 3D, to accurately represent the geometry and material properties.

Each finite element is characterized by a set of mathematical equations describing the local behavior of the material or structure under examination. These equations are applied to individual elements, taking into account various factors. Subsequently, the equations are numerically solved through sophisticated iterative methods, providing an accurate representation of the overall behavior of the system under examination.

In the context of thermal bridges, the use of FEM allows for the precise modeling of heat flow through building materials, considering various environmental and design conditions. This advanced approach enables technicians to identify and correct any weaknesses in a building’s thermal insulation, thus improving its overall energy performance.

With this methodology, technicians can analyze the thermal behavior of a system in detail, assessing the effect of different configurations and materials on the building’s energy efficiency. In this way, building designs can be optimized to reduce heat losses and improve occupant comfort, thus contributing to the creation of more sustainable and energy-efficient environments.

## Technologies and Software Tools

Finite Element Analysis (FEA) is a computational methodology used to conduct complex engineering analyses through software. This approach is based on the Finite Element Method (FEM), which aims to discretely and approximately solve general systems of partial differential equations (PDEs).

Currently, there are numerous software options for finite element analysis, both free and commercial. These software packages divide the analysis process into three phases:

1. Pre-Processing: During this phase, the finite element model is constructed, selecting the type of analysis to be performed, the type of finite elements, defining material parameters, creating discretization, and applying boundary and load conditions;
2. Processing: This is where the actual finite element problem is solved;
3. Post-Processing: In this phase, the analysis results are processed and represented, both in terms of fundamental quantities and derived quantities.

For calculating the linear thermal transmittance of thermal bridges, the use of finite element analysis is fundamental.

The calculation solvers used by the software allow for quick determination of the linear thermal transmittance of thermal bridges, evaluation of thermal flow and thermal coupling coefficient, and verification of bridge correctness. The software also offers tools for intuitive result visualization and interpretation, through contour plots, isotherms, and more.

Detailed analyses of thermal bridges can be performed, evaluating a wide range of combinations and finding optimal solutions to improve building energy efficiency. The speed and ease of use make it a valuable tool for engineers and designers involved in optimizing building thermal performance.

## Advantages and Disadvantages of FEM Analysis

The advantages of finite element analysis include:

• Complex geometries: The ability to handle complex geometries is one of the main strengths of FEM methods;
• Wide applicability: It is suitable for a wide range of engineering problems, including solid mechanics, fluid mechanics, heat transfer, electrostatics, etc.;
• Handling complex constraints and loads: It can easily handle complex boundary and loading conditions.

The disadvantages of finite element analysis are:

• Non-parametrizable solutions: It is not always possible to obtain a closed and parametrizable solution to the problem;
• Inherent approximations: The finite element approach involves approximations in the solution;
• Discretization errors: Errors may occur in the discretization of non-regular domains;
• Interpolation errors: Errors may arise during the interpolation of the solution within finite elements;
• Numerical errors: Errors can occur due to computational limitations, such as the finite number of significant digits and the difficulty in handling extremely large or small numbers;
• Modeling errors: Modeling errors are common and can affect analysis results.

## How to Use Software for Thermal Bridge Calculation

In this video, you can see how to use a software for thermal bridge calculation that utilizes the FEM methodology, designing structures identical to real conditions and obtaining highly professional results.