Optimal preliminary design of variable section beams criterion

Abstract

The present paper discusses about optimal shape solution for a non-prismatic planar beam. The proposed model is based on the standard Timoshenko kinematics hypothesis (i.e., planar cross-section remains planar in consequence of a deformation, but it is able to rotate with respect to the beam center-line). The analytical solution for this type of beam is thus used to obtain deformations and stresses of the beam, under different constraints, when load is assumed as the sum of a generic external variable vertical one and the self-weight. The solution is obtained by numerical integration of the beam equation and constraints are posed both on deflection and maximum stress under the hypothesis of an ideal material. The section variability is, thus, described assuming a rectangular cross section with constant base and variable height which can be described in general with a trigonometric series. Other types of empty functions could also be analyzed in order to find the best strategy to get the optimal solution. Optimization is thus performed by minimizing the beam volume considering the effects of non-prismatic geometry on the beam behavior. Finally, several analytical and numerical solutions are compared with results existing in literature, evaluating the solutions’ sensibility to some key parameters like beam span, material density, maximum allowable stress and load distribution. In conclusion, the study finds a critical threshold in terms of emptying function beyond which it is not possible to neglect the arch effect and the curvature of the actual axis for every different case study described in this work. In order to achieve this goal, the relevance of beam span, emptying function level and maximum allowable stress are investigated.

Research on 3D Measurement and Rapid Location Technique for Assembling the Special-Shaped Structural Segments

“…After the coordinate data of feature points of each segment are obtained by measuring the P 1 -P 3 coordinates, connection interface feature points of the i−1 th and i th segments will be projected onto the interface plane, to calculate the deviation D i of angular point misalignment between upper and lower segments. The objective function is constructed according to Equation (9).…”

“…During the installation and positioning of these specialshaped segments, it is crucial to ensure the axial deviation of the segment within permissible limits [8,9]. The axis, serving as a virtual control target, cannot be measured directly.…”

Cutting Stock Problem (CSP) applied to Structural Optimization for the minimum waste cost

“…Respect to traditional optimization approaches (i.e [17]- [18]) in which the OF represents the total weight of the structure as a sum of the mass of each element, in this study the target function has been evaluated by computing the amount of steel requested during the production phase. A ten-bar truss, comes from [19], has been adopted as case study for the application of the proposed method.…”

A two-stage adaptive penalty method based on co-evolution for constrained evolutionary optimization

“…Many optimization problems in both academia and industry, such as structure optimization [1][2][3], production scheduling [4], and battery model optimization [5], involve constraints. These constrained optimization problems (COPs) can be formulated as follows: minimize f (x), x = (x 1 , x 2 , .…”