{"id":12967,"date":"2025-01-05T10:01:10","date_gmt":"2025-01-05T09:01:10","guid":{"rendered":"https:\/\/maschinenkanzlei.de\/what-does-fem-finite-element-mean-expert\/"},"modified":"2025-06-16T11:18:45","modified_gmt":"2025-06-16T09:18:45","slug":"what-does-fem-finite-element-mean-expert","status":"publish","type":"post","link":"https:\/\/maschinenkanzlei.de\/en\/what-does-fem-finite-element-mean-expert\/","title":{"rendered":"What does FEM (Finite Element Method) mean in engineering?"},"content":{"rendered":"\t\t
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What is this article about?<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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The finite element method (FEM) is one of the most important tools for assessing and optimizing components and entire structures today. Its importance ranges from the automotive industry to aerospace engineering and mechanical engineering, where it has become indispensable in the dimensioning and analysis of components. With its help, even highly complex structures can be calculated efficiently and precisely. <\/p>

Despite its performance, FEM also brings challenges. Its application requires in-depth specialist knowledge, as the quality of the results depends largely on the correct definition of the boundary conditions, the material properties and the model assumptions. In practice, however, the method is often used as a “black box” because modern software greatly simplifies the execution of calculations. This means that <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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the necessary expert knowledge is not always fully available \u2013 a risk that should not be underestimated.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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This article offers a compact insight into the basics of the finite element method and aims to make this fascinating technique understandable for those with a technical interest. From the principles of discretization to modeling and analysis of the results, it shows how the FEM works and why it is indispensable for modern engineering practice. Part 2<\/a> provides further information on the possible errors in the analysis. <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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finite element method<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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A brief summary of the procedure<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/header>\n\t\t\t\t

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What does FEM \/ Finite Element Method mean?<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Figure 1 shows a structure that had failed in reality and Figure 1 shows the pictorial representation of the principal stresses in the affected cross-section determined using the Finite Element Method (FEM).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Figure 1: Fractured structure investigated by FEM.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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When comparing Figure 1 and Figure 1, it is immediately apparent that significant stress increases were also identified in the analysis in the fractured area of the structure. With correct application of the FEM, known external loads, expert model creation and subsequent analysis and evaluation, the FEM allows such problems to be identified in advance. <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Figure 1: Maximum principal stresses for structure according to Figure 1.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Review \/ History of the FEM \/ Finite Element Method<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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The history of the finite element method<\/a> was first introduced and implemented by NASA in the 1960s. In the 1970s, the first analyses began with very simplified calculation models in the aerospace and automotive industries. Until the 1990s, only mainframe computers were required for this and the method was used almost exclusively in the automotive and aerospace industries. <\/p>

For other industries, calculations on mainframe computers were simply too expensive and specialists were not available on the open market. It was therefore necessary to check very carefully what was to be analyzed, because it cost money. <\/p>

Since the mid-1990s, affordable and increasingly faster computers have made FEM applicable to many areas of industry.<\/p>

Software manufacturers took advantage of this boom by promising that almost everything would be predictable and that anyone could use the programs \u2013 a message that continues to shape the industry to this day.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Aim and purpose of FEM simulation<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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The FEM (Finite Element Method) is a numerical method that plays a central role in mechanical engineering. Its aim is to solve complex physical problems that occur in technical components and systems using computer simulations. <\/p>

The finite element method is an indispensable tool for mechanical engineers. It enables detailed and precise analysis of components and systems, which leads to more efficient product development and higher quality when this method is applied correctly. <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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FEM calculation in mechanical engineering in four steps<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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The FEM calculation in mechanical engineering follows four central steps that systematically provide numerical approximate solutions:<\/p>

  1. Model preparation:<\/strong> The component is broken down into small “finite elements”, e.g. hexahedrons or tetrahedrons. The mesh fineness has a decisive influence on accuracy and computing time. <\/li>
  2. Parameter definition:<\/strong> Material properties, external loads and boundary conditions are specified. These determine the behavior of the model under load. <\/li>
  3. Calculation:<\/strong> The FEM software solves a complex system of equations that describes all interactions between nodes and elements. Iterative methods are used for nonlinear problems. <\/li>
  4. Postprocessing:<\/strong> Results such as stress distributions, deformations or temperature fields are evaluated graphically and numerically. Critical areas are analyzed and plausibility checked. <\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    model creation<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    The structure to be assessed is divided into a finite number of small and simple geometric elements (\u201cfinite elements\u201d) that are connected to each other at their nodes (Figure 2). This is based on a complex mathematical system of equations. Once \u201cboundary conditions\u201d have been defined, the deformations and, from this, the strains and stresses can be determined. <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Figure 2: FEM mesh of a laundry drum.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    What is essential is:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Any deformable body is broken down into individual, finite parts, which are called \u201cfinite elements\u201d. <\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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    These finite elements are connected to each other at the so-called nodes (Figure 4). The decisive, continuously changing quantities of the problem are represented by their values at the nodes. Continuous functions are replaced by a system of a finite number of node parameters. The solution of the individual parts ultimately results in the approximate solution for the idealized overall structure. <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Figure 3: Ideal volume model of hexahedral elements with the nodes.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    For different problems, there are different elements, for whose node displacement mathematical approach functions are defined that influence the result. Anyone who is not familiar with this as a \u201csoftware user\u201d cannot even <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    not objective<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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    evaluate.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    influence of the elements<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    A distinction is made between one-dimensional, two-dimensional and three-dimensional elements.<\/p>

    One-dimensional elements are beams and rods, which can often only be used for very simplified questions.<\/p>

    \u201c Thin<\/em> \u201d structures are represented with two-dimensional shell elements. We speak of \u201c structurally thin<\/em> \u201d when one dimension is much smaller than the other two dimensions. The hood of a car, for example, is a classic structurally \u201cthin\u201d structure. <\/p>

    Structures that must be captured using volume elements include bearing blocks, rollers, engine housings, etc.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Figure 4: Linear shell elements (2D) and volume elements (3D).<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    Figure 4 shows common elements for thin structures (2D) and for volumes (3D).<\/p>

    All elements in Figure 4 are linear elements. There are also elements with higher approaches. The differences are discussed in Part 2 of the topic. <\/p>

    As can be seen in particular in Figure 2 ” FEM mesh of a washing drum<\/em> “, in reality it is by no means the case that the elements used have an identical regular boundary. The elements are adapted to the contours of the structure of the component to be assessed (“construction”). As a result, flat quadrilaterals sometimes degenerate into a quadrilateral with different edge lengths, a rhombus or a curved structure if all four nodes do not lie exactly in one plane. <\/p>

    This affects the analysis result and the accuracy of the numerical solution.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Networking and its influence<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    With a finer discretization (mesh fineness), the approximate solution theoretically converges to the (exact) solution, which, however, is based (only) on analytical approaches, which also represent approximate solutions.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Figure 5: FEM mesh of a drum fold with 2D shell elements.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    However, a finer mesh with lower-quality tetrahedral elements does not provide \u201cmore accurate\u201d results than a coarser mesh with higher-quality elements.<\/p>

    The precise knowledge of the elements and, in addition, a technically high-quality discretization (networking) provide the necessary basis for an analysis result with good information quality.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Figure 6: Von Mises equivalent stresses for a model according to Figure 5.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    In principle, it is possible to visualize stresses and displacements in a structure while taking into account bearing boundary conditions and external loads. This is shown in Figure 6 for the model in Figure 5. It should never be forgotten that these are approximate solutions. <\/p>

    Important:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Often an optimal element division can only be achieved through appropriate experience!<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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    It is precisely this fact that creates great potential for error when users work with this finite element method without having detailed knowledge of the underlying technical mechanics, mathematics, physics and materials science.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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    Determining the stress on components and structures using FEM<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    At this point, we would like to briefly explain to laypeople how the risk of mechanical damage to components can be checked.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Figure 7: Necessary information for technical assessment.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    Three<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    necessary criteria<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    are important for the assessment (Figure 7):<\/p>

    1. First of all, any form of mechanical damage requires that external loads<\/em> (forces, pressures, temperatures, etc.) act on the component.<\/li>
    2. The external load<\/a> results in stresses<\/em> in the structure. These must be known or determined. The finite element method ( FEM<\/a> ) is suitable for this. This is marked with the number 2 in Figure 7. <\/li>
    3. If these internal stresses are known, they can be compared with the mechanical properties<\/em> of the material used. If the corresponding stresses occurring in the material are greater than or equal to the mechanical properties of the material used, the component can fail due to different types of failure depending on the type of load (static, dynamic). <\/li><\/ol>

      What is essential, however, is that the external load is known and, above all, what results from it in the component. This in turn requires that the other boundary conditions are also known for an analysis. With the finite element method, bearing boundary conditions must be selected in order to obtain a result. <\/p>

      Important:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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      The external loads and the support boundary conditions also influence the result of the finite element method.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

      \n\t\t\t
      \n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
      \n\t\t\t\t\t\t
      \n\t\t\t\t\t
      \n\t\t\t
      \n\t\t\t\t\t\t
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      \n\t\t\t\t\t

      areas of application in mechanical engineering<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      The finite element method (FEM) is indispensable in mechanical engineering and is used in numerous classic application areas, including:<\/p>

      1. structural mechanics<\/strong>