Abstract
In this article, the dependency between different elements in solid structures is considered and a substructure-based interval finite element method is used to model the interval properties. The penalty method is applied to impose the necessary constraints for compatibility. In order to obtain the interval stresses, an approximation solution based on the Taylor expansion method is presented. Then, the proposed interval substructure model is expanded to nonlinear problems. In consideration of the nonlinear property of the elasticity modulus, an interval elastoplastic substructure analysis method using constant matrix based on the incremental theory is proposed and the interval expression of the interval stress updated formation is derived. Finally, numerical examples are carried out to demonstrate the reasonability and feasibility of the proposed method and evaluation system.
Highlights
The concept of uncertainty plays an important role in the investigation of various sciences and engineering problems.[1]
The EBE-based interval finite element method (EBE-IFEM) was extended to calculate the envelope frequency response functions with uncertain parameters by Yang et al.,[13,14] and the results indicated the effectiveness of the EBE model to frame structures
The results show that the Sub-IFEM provides sharper enclosures of the vertex method compared to the EBE-IFEM
Summary
The concept of uncertainty plays an important role in the investigation of various sciences and engineering problems.[1]. The EBE-based interval finite element method (EBE-IFEM) was extended to calculate the envelope frequency response functions with uncertain parameters by Yang et al.,[13,14] and the results indicated the effectiveness of the EBE model to frame structures. The use of the EBE model in this situation increases the occurrences of the same parameters, which will overestimate the interval results. The situation that the number of the same intervals increases with the number of the elements intensifies the expansion of the results To overcome this drawback, the substructure method is used to decrease the multi-occurrence of the same intervals. When invoking the dependency of variables, elements of the same parameters can be treated as a substructure, and the global matrix can be obtained as follows based on different substructures
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