Size and Shape Optimization of Space Trusses Considering Geometrical Imperfection-Sensitivity in Buckling Constraints

Abstract

Optimal design considering buckling of compressive members is an important subject in structural engineering. The strength of compressive members can be compensated by initial geometrical imperfection due to the manufacturing process; therefore, geometrical imperfection can affect the optimal design of structures. In this study, the metaheuristic teaching-learning-based-optimization (TLBO) algorithm is applied to study the geometrical imperfection-sensitivity of members' buckling in the optimal design of space trusses. Three benchmark trusses and a real-life bridge with continuous and discrete design variables are considered, and the results of optimization are compared for different degrees of imperfection, namely 0.001, 0.002, and 0.003. The design variables are the cross-sectional areas, and the objective is to minimize the total weight of the structures under the following constraints: tensile and compressive yielding stress, Euler buckling stress considering imperfection, nodal displacement, and available cross-sectional areas. The results reveal that higher geometrical imperfection degrees significantly change the critical buckling load of compressive members, and consequently, increase the weight of the optimal design. This increase varies from 0.4 to 119% for different degrees of imperfection in the studied trusses.

Teaching-Learning Based Optimization Method Considering Buckling and Slenderness Restriction for Space Trusses

“…where, 𝐸 is the elastic modulus of the material, 𝐼 is the moment of inertia of the cross section, 𝐿 is the length of the column, 𝜆 is the slenderness index, 𝑟 is the radius of rotation of the bar, 𝑃 𝑐𝑟 is the critical buckling load and 𝜎 𝑐𝑟 is the critical buckling stress. Therefore, the column will buckle around the axis with the lowest moment of inertia [12].…”

“…Fig. 3 25-bar tower, [4] Table 1 Applied Loads on the 25-bar tower, [12] Node Fx (kN) Fy (kN) Fz (kN) The optimization results are shown in table 2. To validate the code, the case addressed by Camp and Farshchin [4] was applied without applying the buckling restrictions.…”

“…Haghpanah and Foroughi [12] analyzed the optimization of space trusses using the TLBO method considering critical buckling load restriction values and their percentages to simulate imperfection effects.…”

Mechanical Properties Analysis of Bilayer Euler-Bernoulli Beams Based on Elasticity Theory

“…Haghpanah [4] and Laminou [5] found that the structure size and load would have a significant impact on the mechanical properties of the mechanical systems. Hence, a lot of work has been undertaken to explore the mechanical properties of beams.…”