Response of shape optimization of thin-walled curved beam and rib formation from unstable structure growth in optimization
- 73 Downloads
A thin-walled curved beam is a complex structure. Sectional deformation occurs due to induced out-of-plane force when the beam is bent. Bending stiffness is significantly lowered due to this deformation. Installation of ribs to support this induced force is often an effective countermeasure to ensure stiffness. This study examined shape optimization of an I-sectional curved beam. Ribbed structures were successfully created from non-ribbed structures by adding humps to the initial structure. It was discovered that instability of the shape optimization occurs under the influence of the induced force. Here, ‘instability’ refers to the amplification of initial perturbations similar to buckling phenomena. In the present case, the humps grew and formed ribbed structures. The bending stiffness of the ribs was significantly improved. In addition, simple thickening of flange parts also effectively improves the bending stiffness. As these two structural improvements progress simultaneously, branching of the optimization occur. This branching depends on the given volume constraint. A parameter study targeting volume observed branching to ribbed or thickened non-ribbed structures. This instability enables a leap from a non-ribbed to a ribbed structure in the optimization.
KeywordsCurved beam Induced force Shape optimization Rib Instability
The present work did not receive any specific grants from funding agencies in the public, commercial, or not-for-profit sectors.
- Azegami H (2004) Solution to boundary shape optimization problems. In: Brebbia CA, de Wilde WP (eds) High performance structures and materials II. WIT Press, Southampton, pp 589–598Google Scholar
- Azegami H (2006) Solution to boundary shape identification problems in elliptic boundary value problems using shape derivatives. In: Tanaka M, Dulikravich GS (eds) Inverse problems in engineering mechanics II. Elsevier, Tokyo, pp 277–284Google Scholar
- Azegami H, Kaizu S, Shimoda M, Katamine E (1997) Irregularity of shape optimization problems and an improvement technique. In: Hernandez S, Brebbia CA (eds) Computer aided optimization design of structures V, vol 28. Computational Mechanics Publications, Southampton, pp 309–326Google Scholar
- Azegami H, Wu ZC (1996) Domain optimization analysis in linear elastic problems: approach using traction method. JSME Int J, Ser A 39:272–278Google Scholar
- Chancharoen W, Azegami H (2018) Topology optimization of density type for a linear elastic body by using the second derivative of a KS function with respect to von Mises stress. Struct Multidiscip Optim (issued on line: https://doi.org/10.1007/s00158-018-1937-z)
- Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of the 1995 IEEE conference on neural networks, IV. Piscataway, pp 1942–1948Google Scholar
- Shimoda M, Tsuji J, Azegami H (2007) Non-parametric shape optimization method for thin-walled structures under strength criterion. WIT Transactions on the Built Environment (Computer Aided Optimum Design in Engineering X) 91:179–188Google Scholar
- Shintani K, Azegami H (2014) A design method of beads in shell structure using Non-Parametric shape optimization method. ASME Proceedings 34th Computers and Information in Engineering Conference 1A:17–20Google Scholar
- Timoshenko S (1923) Bending stresses in curved tubes of rectangular cross-section. Trans ASME 45:135–140Google Scholar
- Timoshenko S (1955) Strength of materials part I elementary, section 84. Bending of curved tubes. Van Nostrand ReinholdGoogle Scholar