Using Minimum Actuators to Control Shape and Stress of a Double Layer Spherical Model Under Gravity and Lateral Loadings

Abstract

Spherical domes are picturesque structures built in developed countries to attract tourists. Due to horizontal and vertical overloading, the structures' attractive shapes may be disturbed, and some members' stress may exceed the elastic level. In this paper, the shape and stress of a deformed double-layer spherical numerical model due to simultaneous lateral and vertical loadings are controlled, meanwhile, the number of actuators to alter the length of active members is minimized. The nodal displacements of the outer shape of the numerical model of the double-layer spherical structure are nullified. In addition, the stress of the members of the structure was monitored to stay within the elastic level. Moreover, the number of used actuators was minimized. These objectives are done by subjecting controlling formulations to a function that finds the minimum of constrained nonlinear multivariable which is called fmincon. The defined function in MATLAB uses one of the optimization algorithms (sequential quadratic programming, interior point, trust-region reflective, and active set). The algorithms search for active members that have a significant influence in controlling the targeted joints and members. Furthermore, the algorithms exclude the inactive actuators in several loops. The results obtained from MATLAB program are validated by SAP2000 software.

A Review of Nonlinear Control Strategies for Shape and Stress in Structural Engineering

“…Nonlinearities are brought about by geometric complications, particularly when working with thin structures or substantial deformations [41][42][43]. The effect of geometric nonlinearities may be ignored by traditional linear analysis, which could result in inaccurate predictions of structural reactions [4,6,8,45,[50][51][52]. To accurately represent the behavior of structures under different loads, sophisticated geometrically nonlinear models are essential [53].…”

“…This requirement is demonstrated by beams [16,29,[87][88][89][90][91][92][93][94][95], trusses [9,[96][97][98][99][100][101][102][103], and frames [104][105][106] by linear or nonlinear methods, where the exact placement of structural components guarantees the effective distribution of loads while maintaining structural integrity. In addition, the sphere [6,8,52,107,108], antenna structures [100,109,110], egg-shaped structure [4], and dome [3,5,15,111] constructions are examples of architectural achievements where geometric precision combines with esthetic appeal and practicality to create memorable areas and famous structures. While cable structures [3, 10-13, 30, 31, 103, 112-119] challenge preconceived concepts of stability and balance with their intricate designs, cable structures, with their elegant curves and tensioned forms, epitomize the union of engineering genius with artistic harmony.…”

“…These strategies demonstrate the versatility and adaptability of concurrent shape and stress control methodologies, ranging from adaptive building facades that dynamically respond to environmental conditions [7,10,11,31,132] while managing stress to aerospace structures that optimize both aerodynamics and structural integrity [146,147]. There are some examples of combined form and stress control, such as beams, trusses [2,9,97,98,101,103,148], spheres [6,8,52], antenna structures, cable structures [30,31,103,115,116], and domes [5,111] by linear [6,8,9,52,97,98,101,148] or nonlinear [30,31] methods. The mentioned examples highlight successful implementations and offer insightful information on the efficacy and practicality of stress control techniques [2,5,6,8,9,30,31,52,97,98,101,…”

“…There are some examples of combined form and stress control, such as beams, trusses [2,9,97,98,101,103,148], spheres [6,8,52], antenna structures, cable structures [30,31,103,115,116], and domes [5,111] by linear [6,8,9,52,97,98,101,148] or nonlinear [30,31] methods. The mentioned examples highlight successful implementations and offer insightful information on the efficacy and practicality of stress control techniques [2,5,6,8,9,30,31,52,97,98,101,115,116,119,120,[148][149][150].…”

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

“…The optimal design was done for I-and H-shaped crane bridge girders [36], reinforced concrete sections [37], and steel moment frames [38]. Moreover, the significance of the most active members' location to change the bars' lengths to reshape and redistribute stress in members was also studied [39][40][41][42][43]. So far, studies have not been carried out either to control bending moment in beams or to beam size optimization for space frames.…”