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The article presents methods based on the Additional Finite Element Method (AFEM) used to resolve the main problems of analyzing N-nonlinear systems. This method is an extended variant of the Finite Element Method (FEM) used to calculate systems with several physical nonlinear properties at ultimate limit states. AFEM adds extended numerical Elastic Solutions Method (ESM) and constructive Limit State Method (LSM) operations to the traditional sequence of FEM. The main set of equations changes according to the growth of external load and quantity of nonlinear properties. The last step corresponds to the ultimate limit state of the system. At this moment the load is maximal and stiffness is minimal. The initial system is transformed into an ideal failure model (IFM). Additional design diagrams (ADDs) and additional finite elements (AFEs) implement this operation mathematically. This method connects numerical FEM and constructive LSM, expanding the application of FEM through the use of the AFEM numerical algorithm.

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AFEM as the Way to New Extended FEM Algorithms for Analysis of N-nonlinear Systems at Limit States

  • 会议论文

  • 发表日期：

    2026年

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  • A. Ermakova

摘要

The article presents methods based on the Additional Finite Element Method (AFEM) used to resolve the main problems of analyzing N-nonlinear systems. This method is an extended variant of the Finite Element Method (FEM) used to calculate systems with several physical nonlinear properties at ultimate limit states. AFEM adds extended numerical Elastic Solutions Method (ESM) and constructive Limit State Method (LSM) operations to the traditional sequence of FEM. The main set of equations changes according to the growth of external load and quantity of nonlinear properties. The last step corresponds to the ultimate limit state of the system. At this moment the load is maximal and stiffness is minimal. The initial system is transformed into an ideal failure model (IFM). Additional design diagrams (ADDs) and additional finite elements (AFEs) implement this operation mathematically. This method connects numerical FEM and constructive LSM, expanding the application of FEM through the use of the AFEM numerical algorithm.