Development of Single-Node Finite Elements for the Calculation of Systems with Unilateral Constraints by FEM in the Form of the Classical Mixed Method

This article investigates the features and advantages of using single-node finite elements of Finite Element Method in the form of the Classical Mixed Method. The research was conducted on one-dimensional problems with various types of unilateral constraints (rigid, elastically flexible, with a gap between the structure and the support). A special algorithm for switching the condition of the support was developed by modifying the response matrix of the single-node finite elements. This algorithm allows switching of connections without changing the calculation scheme of the structure. Verification was carried out by comparing the calculated results with the results of the calculation of the LIRA SAPR software package, which calculation schemes are built using single-node finite elements that implement the displacement method. The article demonstrates the advantages of solving problems that include single-node finite elements that simulate various types of constructive nonlinearity, including ease of algorithmization in the decision-making area on switching the state of unilateral constraints, due to the inclusion in the response matrix of both the force that arises in the connection and displacement along its direction, and the ability to solve the problem of elastic connection, which is included in the work after the section gap reaches a certain value.