Mathematical proof of strength

The strength verification is a procedure in which the strength and structural integrity of components or assemblies is verified by calculations. This process is an essential part of engineering and is used to ensure that designs meet safety, reliability and performance requirements.

The finite element method (FEM) is a frequently used tool for the computational strength analysis. The FEM is a numerical method that makes it possible to divide complex structures into smaller, simpler parts, so-called finite elements. These elements are then analyzed to simulate the behaviour of the entire structure under different load conditions. By using FEM, engineers can calculate and evaluate stresses, deformations and other mechanical properties of components.

The computational strength verification comprises several steps. First, a detailed model of the structure is created, taking into account the geometry, material properties and boundary conditions. The loads and load cases to which the structure is exposed during operation are then defined. These load cases can include static or dynamic loads caused by forces, moments, temperatures or other influences.

The stresses and deformations in the structure are then calculated using FEM or other calculation methods. These results are compared with the permissible values, which are defined by material properties and safety factors. If the calculated stresses and deformations are within the permissible limits, the proof of strength is deemed to have been provided.

The computational strength verification offers several advantages. It enables a detailed and precise analysis of structures without the need to build physical prototypes. This saves time and costs and enables faster and more efficient product development. In addition, computational verification allows potential weaknesses in a design to be identified and rectified at an early stage, increasing the reliability and safety of the end products.

In summary, it can be said that the computational strength analysis is an indispensable tool for the design and analysis of components and systems. By using modern calculation methods such as FEM, engineers can ensure that their designs can withstand the demands of operation and can be operated safely.