Question 2 a) Name the two major structural topology optimisation techniques and describe the major differ- ences between them. Propose a topology optimisation problem relevant to your programme of study, suggest two suitable methods for solving it, compare and contrast the major features of these methods. [12 marks] b) Describe the major techniques used for structural size optimisation. Provide an example of a structural size optimisation problem relevant to your programme of study. [13 marks] Consider the two-beam problem shown in Figure 2. The beams are both of length L 1 m and have material with modulus of elasticity E-200 GPa. Beam 1 has moment of inertia I-2 x 10-1 m and beam 2 has I=1 x 10-4 m. The same downward distributed force of 1 kN/m is applied across the two beams. m 1 kN/m 1 kN/m Beam 1 1m Beam 2 2 m Figure 2: Beam bending problem domain. c) Using two elements to resolve the two-beam sections, solve the displacement problem and find the rotations and displacements at the three points of the two beams. [17 marks] d) From your answer to part c), sketch the solution for the displacement of the bars along their length. Explain where the greatest displacements occur, and whether the displacement is sym- metric. Relate your explanation to the problem set up. [8 marks]