First assignment for the exam

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Lightweight design of mechanical structures Homework report Optimum design of a channel beam Chiara Moreschini ID 10601144 Points Correctness of the formulation of the optimum design problem /7 Correctness of the solution /8 Ability of discussing critically results /10 Quality of the presentation /5 Chiara Moreschini – ID 10601144 1 1. Problem description The structure to be optimized is a C-section cantilever beam constrained at one end, with length L=2100mm and a vertical load P applied to the free end equal to 1,0 kN. The beam has the following characteristics: Figure 1: Geometric characteristics of the beam 𝑘=𝑤−2𝑡 (𝐶!=𝑤2 𝐶"=2ℎ#𝑡+𝑘𝑡#2ℎ𝑤−𝑠𝑘(ℎ−𝑡) ⎩⎨⎧𝐼!=2𝑡ℎ$+𝑘𝑡$3−(2𝑡ℎ+𝑘𝑡)𝐶"# 𝐼"=ℎ𝑤$−𝑘$(ℎ−𝑡)12 Where (Cx, Cy) are the centroid’s coordinates with respect to the initial reference system (Xc, Yc), while Ix and Iy are the moments of inertia of the cross-section about the new (X,Y) reference system centered in C. 2. Data and information collection Table 1: Mechanical properties of S355J0 The beam is made of steel S355J0, which is a structural steel with the mechanical properties reported in Table 1. C-section beams produced with this kind of steel are usually manufactured by hot rolling. 3. Definition of design variables The design variables are the dimensions of the section of the beam: thickness (t), width (w) and height (h). 4. Optimization criterion The objective function that has been chosen is the volume: 𝑉=[𝑤ℎ−𝑘(ℎ−𝑡)]∙𝐿 [𝑚𝑚$] Since the material has not been considered as a design variable, it is equivalent to use the volume or the mass as objective function, but since the mass requires an additional parameter to be computed (the density), volume has been used as objective function. Also the area of the cross-section could have been chosen as objective function, since the…