{"id":13208,"date":"2025-02-10T12:35:14","date_gmt":"2025-02-10T11:35:14","guid":{"rendered":"https:\/\/maschinenkanzlei.de\/finite-element-analysis-error-expert\/"},"modified":"2025-07-21T15:47:36","modified_gmt":"2025-07-21T13:47:36","slug":"finite-element-analysis-error-expert","status":"publish","type":"post","link":"https:\/\/maschinenkanzlei.de\/en\/finite-element-analysis-error-expert\/","title":{"rendered":"Finite Element Analysis (FEA) – Error Potential in Mechanical Engineering?"},"content":{"rendered":"\t\t
\n\t\t\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
\n\t\t\t\t
\n\t\t\t\t\t

What is this article about?<\/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

Finite element analysis (FEA) is a powerful tool in mechanical engineering. But what happens when it is used incorrectly? Recipients of analysis reports and the engineers who carry them out rely on their calculations to make structures safer, more efficient and more durable. But this is precisely where risks lurk: Inaccurate modeling, incorrect assumptions and incorrect interpretations can lead to catastrophic errors. <\/p>\n

How can such errors be avoided? What factors influence the accuracy of simulations? This article highlights the most common stumbling blocks in FEA – and shows how engineers can achieve more precise, reliable results. <\/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

\n\t\t\t\t\t\t\t
<\/div>\n\t\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t
Finite Element Analysis<\/div>\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

A short summary and potential for error<\/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

\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t

Faulty Finite Element Analysis (FEA) - A Growing Problem in Litigation<\/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

In recent years, legal disputes and pre-trial disputes in connection with faulty finite element analyses (FEA) have increased noticeably. As an expert in the analysis of causes of damage, vibration technology and operational stability of machines and their components, I have found that both the lawyers of the disputing parties and the courts are often unaware of the amount of effort that actually goes into such an analysis. Proving that an analysis is faulty is complex, but undoubtedly possible, although usually costly. <\/p>

Furthermore, simply looking at the usual \u201ccolorful analysis pictures\u201d is not enough to provide reliable evidence of a possible analysis error in a legal dispute as a court expert or in a legal dispute as a party expert.<\/p>

A central problem lies in the increasing popularity and supposed “easy application” of the finite element method (FEM). Modern software solutions suggest that such analyses can be carried out quickly and easily – sometimes even directly in CAD programs. The reality, however, is different: many users do not have the necessary mechanical, numerical and material engineering expertise to correctly interpret the results of a finite element analysis and avoid critical errors. <\/p>

The result is numerous incorrect analyses in reality. This often goes unnoticed because in many cases “high stresses” are detected, which in practice often leads to over-dimensioned components – an economic problem, but usually not a safety-critical one. However, it always becomes critical when components are to be designed in borderline areas and an incorrect calculation leads to structural failure or even major damage. <\/p>

Legal disputes in particular show that a careful, methodically correct analysis is essential. The quality of an FEA depends on the professional competence of the user – and this is precisely where an often underestimated risk lies. <\/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

\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t

What does FEM \/ Finite Element Method mean?<\/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

Part 1<\/a> of this article deals with the finite element method<\/a> and explains some of the basics of FEM. There will be no repetition here. <\/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

\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t

What does FEA \/ Finite Element Analysis mean?<\/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

Finite Element Analysis (FEA) is a powerful numerical method that enables engineers to simulate and predict the behavior of components and systems within the framework of numerical approximate solutions. It is based on the finite element method (FEM), a mathematical technique that makes complex problems analyzable by breaking them down into smaller, manageable subproblems. While FEM provides the underlying methodology, FEA includes the <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\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\t<\/div>\n\t\t<\/div>\n\t\t\t\t
\n\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t

practical application process as well as the interpretation of the results generated by the FEM calculations.<\/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
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t

The FEM breaks down a complex system into a multitude of small, simple units, the so-called \u201celements\u201d.<\/p>\n

These finite elements are connected to each other at their nodes (Figure 1). Behind this is a complex mathematical system of equations. Once the “boundary conditions” 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

\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\"FEM\t\t\t\t\t\t\t\t\t\t\t
Figure 1: 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
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t

The calculations take into account material properties, geometric configurations and external influences such as loads or temperatures.<\/p>

Finite element analysis (FEA) serves as a crucial tool in engineering. By using FEA, development times can be shortened, costs reduced and risks minimized. Instead of physical prototypes, virtual models are used that can be tested under a wide range of operating and environmental conditions. This not only reduces the use of resources, but also increases the safety and efficiency of the development process if the method is used correctly. <\/p>

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

The FEA must be carried out technically correctly within the framework of approximate solutions.<\/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
\n\t\t\t\t
\n\t\t\t\t\t

Process of FEA \/ Finite Element Analysis 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 process of finite element analysis usually follows the following pattern:<\/p>\n

    \n
  1. Identify and formulate the problem<\/strong><\/li>\n
  2. Define task<\/strong><\/li>\n
  3. Preprocessing: Model preparation:<\/strong> The component is broken down into small “finite elements”, e.g. hexahedrons or tetrahedrons, squares or triangles. The mesh fineness has a decisive influence on accuracy and computing time. Parameter definition:<\/strong> Material properties, external loads and boundary conditions are defined and specified. These determine the behavior of the model under load. <\/li>\n
  4. Analysis:<\/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>\n
  5. Postprocessing:<\/strong> Results such as stress distributions, deformations or temperature fields are evaluated graphically and numerically. Critical areas are analyzed and plausibility checked. <\/li>\n<\/ol>\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
    \n\t\t\t\t\t\t
    \n\t\t\t\t\t
    \n\t\t\t
    \n\t\t\t\t\t\t
    \n\t\t\t\t
    \n\t\t\t\t\t

    Finite Element Analysis (FEA) faulty \/ error potentials<\/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

    Despite its wide acceptance and performance, the application of finite element analysis (FEA) contains potential sources of error that can lead to inaccurate results or misinterpretations. These errors often result from assumptions, simplifications or improper handling of the method. The most important potential errors when applying FEA are listed below: <\/p>\t\t\t\t\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

    Inaccurate modeling<\/h3>\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 influence of the elements was discussed briefly in section 3.2 in part 1<\/a> .<\/p>\t\t\t\t\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

    Which model is correct?<\/h4>\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

    There is the following definition:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

    \n\t\t\t\t\t\t\t
    <\/div>\n\t\t\t\t\t\t\t
    \n\t\t\t\t\t
    \n\t\t\t
    \n\t\t\t\t\t\t
    \n\t\t\t\t
    \n\t\t\t\t\t
    model creation ...<\/div>\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
    No model is \u201cright\u201d.\n Every model only partially reflects reality.\n It depends on the problem which model is suitable to provide the required information with as little effort as possible and yet with sufficient accuracy.\n<\/div>\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
    \n\t\t\t\t
    \n\t\t\t\t\t\t\t\t\t

    Common problems are:<\/p>\n

    Geometric simplifications:<\/strong> To reduce calculation time, simplifications are often made to the model geometry. This can lead to important details such as small radii, holes or specific geometries that affect local stresses not being taken into account. <\/p>\t\t\t\t\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\t\t\t
    \n\t\t\t\t\t\t\t\t\t\t\"Finite\t\t\t\t\t\t\t\t\t\t\t
    Figure 2: Displacements on the half model of a ladder.<\/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
    \n\t\t\t\t
    \n\t\t\t\t\t\t\t\t\t

    Incorrect material properties:<\/strong> Inaccurate or insufficiently tested material data can lead to erroneous results, especially for anisotropic, nonlinear or time-dependent materials.<\/p>\t\t\t\t\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\t\t\t
    \n\t\t\t\t\t\t\t\t\t\t\"fehlerhafte\t\t\t\t\t\t\t\t\t\t\t
    Figure 3: Linear calculation along Hooke's line.<\/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
    \n\t\t\t\t
    \n\t\t\t\t\t\t\t\t\t

    A “classic” case of incorrect analyses is that the calculation continues linearly along the green Hooke’s line<\/em> (red in Figure 3) even beyond the yield point. The hardening is not taken into account and the result is <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\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\t<\/div>\n\t\t<\/div>\n\t\t\t\t
    \n\t\t\t
    \n\t\t\t\t\t\t
    \n\t\t\t\t
    \n\t\t\t\t\t\t\t\t\t

    correct in terms of mathematics, but completely wrong in terms of reality,<\/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
    \n\t\t\t\t
    \n\t\t\t\t\t\t\t\t\t

    because the material properties \u201cabove\u201d the yield point no longer behave linearly (green area) (Figure 3).<\/p>\n

    Unrealistic boundary and load conditions:<\/strong> Assumptions about the actual loads, supports or environmental conditions are often inaccurate. Incorrect assumption or knowledge of the loads can cause significant deviations from reality. <\/p>\t\t\t\t\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\t\t\t
    \n\t\t\t\t\t\t\t\t\t\t\"FEM\t\t\t\t\t\t\t\t\t\t\t
    Figure 4: 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
    \n\t\t\t\t
    \n\t\t\t\t\t\t\t\t\t

    Three<\/p>\t\t\t\t\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

    necessary criteria<\/strong><\/p>\t\t\t\t\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

    are important for the assessment (Figure 4):<\/p>\n

      \n
    1. External loads<\/em> (forces, pressures, temperatures, etc.) act on the component. This is marked with the number 1 in Figure 4. <\/li>\n
    2. The external load results in stresses<\/em> in the structure. These must be known or determined. This is marked with the number 2 in Figure 4. <\/li>\n
    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>\n<\/ol>\n

      What is essential, however, is that the external load is known and, above all, what results from it in the component.<\/p>\t\t\t\t\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

      Numerical errors<\/h3>\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

      When applying the finite element method, one should never forget that the result of a finite element analysis is a numerical procedure.<\/p>\n

      If a result can be generated, then the mathematics is certainly \u201ccorrect\u201d. If this were not the case, no result would be obtained. The crucial question, however, is whether the \u201cresult\u201d is plausible or can be plausible. However, if the model is faulty, then the mathematics can \u201ccalculate correctly\u201d. However, the result is then <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\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\t<\/div>\n\t\t<\/div>\n\t\t\t\t
      \n\t\t\t
      \n\t\t\t\t\t\t
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      mathematically correct but still wrong in reality.<\/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
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      It is therefore the great art to<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\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\t<\/div>\n\t\t<\/div>\n\t\t\t\t
      \n\t\t\t
      \n\t\t\t\t\t\t
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      To know or be able to estimate the error potential in a finite element analysis (FEA).<\/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
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      Discretization:<\/strong> A model mesh that is too coarse (too few or too large elements) may not correctly represent important local effects, such as stress peaks or deformation details. On the other hand, elements that are too small lead to long computing times without always providing a significant gain in accuracy. <\/p>\t\t\t\t\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\t\t\t
      \n\t\t\t\t\t\t\t\t\t\t\"finite\t\t\t\t\t\t\t\t\t\t\t
      Figure 5: An ideal hexahedron model.<\/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
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      Figure 5 shows an analysis model made up of hexahedral elements. These are of \u201chigh quality\u201d. However, they can only be used for rotationally symmetric solid bodies or regular bodies such as cuboids. <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\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\t<\/div>\n\t\t<\/div>\n\t\t\t\t
      \n\t\t\t
      \n\t\t\t\t\t\t
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      However, the reality of technical problems deviates from these ideal geometries.<\/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
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      This alone leads to a decrease in accuracy compared to the quality of the results of hexahedral elements. This will be discussed later in this article. <\/p>\n

      Element types:<\/strong> Choosing inappropriate finite element types (e.g. linear instead of quadratic elements) can have a significant impact on accuracy.<\/p>\n

      Rounding and approximation errors:<\/strong> Numerical calculations are susceptible to rounding errors, especially in complex models with many iterations. These errors can accumulate and distort the results. <\/p>\t\t\t\t\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

      Incorrect interpretation of the results<\/h3>\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

      Over-reliance on simulation results:<\/strong> FEA results are based on assumptions and simplifications and are<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\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\t<\/div>\n\t\t<\/div>\n\t\t\t\t
      \n\t\t\t
      \n\t\t\t\t\t\t
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      always approximate solutions.<\/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
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      Uncritical acceptance of the results without validation through physical tests or experience can lead to wrong decisions.<\/p>\t\t\t\t\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\t\t\t
      \n\t\t\t\t\t\t\t\t\t\t\"Finite\t\t\t\t\t\t\t\t\t\t\t
      Figure 6: Stress peaks on a keyway connection \u2013 boundary condition 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
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      Figure 6 and Figure 7 show an analysis with the same external load but slightly different support conditions. Clearly, one can see significant changes in the determined stresses at the keyway. <\/p>\n

      The question arises: which analysis better reflects reality?<\/p>\n

      Does the layman immediately recognize which solution is likely to be wrong and which is closer to reality? This is precisely the central problem with analyses using the finite element method. Anyone who only sees the color “red” and “searches” at the same time is susceptible to incorrect results, incorrect interpretations and possibly also to “problems” that are not problems at all in reality. <\/p>\t\t\t\t\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\t\t\t
      \n\t\t\t\t\t\t\t\t\t\t\"FEA\t\t\t\t\t\t\t\t\t\t\t
      Figure 7: Stress peaks on a keyway connection \u2013 boundary condition 2.<\/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
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      Neglect of uncertainties:<\/strong> There are numerous real uncertainties that are not and cannot be taken into account in an analysis. For example, the analysis always assumes a stress-free state. This is a fallacy, because <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\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\t<\/div>\n\t\t<\/div>\n\t\t\t\t
      \n\t\t\t
      \n\t\t\t\t\t\t
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      Often, even in the unloaded state, so-called residual stresses are already present in the structure.<\/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
      \n\t\t\t\t
      \n\t\t\t\t\t\t\t\t\t

      The extent of these is often unknown. There are also other influences, such as <\/p>\n