Non-Linear Analysis of Structures Utilizing Load-Discretization of Stiffness Matrix Method with Coordinate Update

Abstract

This paper proposes a stiffness method based structural analysis algorithm for geometrically non-linear structures. In this study, the applied load on the joints has been discretized to a sequence of a few loadings applied. Each loading step produces incremental external nodal displacements, which are added to the corresponding coordinates to get a new geometrical shape of the structure. This process is iteratively repeated until the sum of the loading of all iterations matches the total initial applied loading. The size of the increments affects the technique’s accuracy, subsequently affecting the number of iterations. The configuration of non-linear geometrical structures is vital in the work; a slight change of the coordinates makes a considerable variation of nodal displacements. In this paper, three pin-jointed assemblies and a cantilever beam have been examined using the proposed technique; significantly reasonable outcomes emerged, compared to the non-linear approaches, such as Dynamic Relaxation Method (DRM) and Non-linear approach by Kwan. In a numerical sense, the dissimilarity between the results of the conventional Stiffness Matrix (SM) method and the non-linear method is about 228%, while the maximum discrepancy between the proposed approach and the non-linear methods is just above 15%.

Significance of Single-Interval Discrete Attributes: Case Study on Two-Level Discretisation

“…Among other advantages, the following can be distinguished: lower memory requirements for storage, increased comprehensibility of the description of the presented knowledge [17]-which is more relevant for interpretation-the possible reduction of noise present in the data, and enhanced efficiency of induction algorithms that work on a reduced domain of attribute values, which also influences time needed for operations. However, it should be noted that the discretisation process can cause some loss of information [18]; therefore, it should be used with certain caution and always adjusted to the nature of available data, its characteristics, and inherent nature [19].…”

Nonlinear structural analysis technique based on flexibility method by Pade approximants

“…They utilized the Moore-Penrose pseudoinverse to compute the minimal necessary actuation. Furthermore, Manguri and Saeed [8] , as well as Saeed, et al [10] , proposed an approximate linear force analysis technique. It is based on updating the joint coordinates of the structural geometry in every iteration for the discretized applied load.…”

“…Various recent methods for analyzing cable structures have been thoroughly reviewed [3][4][5][6][7][8][9][10] . Most recent methods insist on algorithmic procedures, computer operation aspects, and programming, which contribute to their prorated complexity.…”

“…Various recent methods for analyzing cable structures have been reviewed, which recently exist thoroughly [3][4][5][6][7][8][9][10] , and are used for both the static and dynamic analysis of structural cables. The susceptibilities of these solution approaches are dissimilar from each other.…”

Bending Moment Control and Weight Optimization in Space Structures by Adding Extra Members in the Optimal Locations

“…Chen and Lui [9] discussed the types of space frames and several analysis methods. Researchers used different methods to analyze space frames, for example, the modified arch length method [10], Euler's finite rotation formula [11], and the stiffness matrix method [12]. Regarding minimizing bending moments in simple frames, Wang [13] suggested a computational technique to reduce flexural moments in frame members.…”