Fundamentals of exact multi-load topology optimization – stress-based least-volume trusses (generalized Michell structures) – Part I: Plastic design

2020

Traditional truss layout optimization employing the ground structure method will often generate layouts that are too complex to fabricate in practice. To address this, mixed integer linear programming can be used to enforce buildability constraints, leading to simplified truss forms. Limits on the number of joints in the structure and/or the minimum angle between connected members can be imposed, with the joints arising from crossover of pairs of members accounted for. However, in layout optimization, the number of constraints arising from 'crossover joints' increases rapidly with problem size, along with computational expense. To address this, crossover constraints are here dynamically generated and added at runtime only as required (so-called lazy constraints); speedups of more than 20 times are observed whilst ensuring that there is no loss of solution quality. Also, results from the layout optimization step are shown to provide a suitable starting point for a non-linear geometry optimization step, enabling results to be obtained that are in agreement with literature solutions. It is also shown that symmetric problems may not have symmetric optimal solutions, and that multiple distinct and equally optimal solutions may be found.

Section: Funding Informationmentioning

confidence: 99%

Layout optimization of simplified trusses using mixed integer linear programming with runtime generation of constraints

Fairclough

2020

“…Using the British Standard load cases (2a-2c), and with Assumptions 1, 2 and 3 removed, a parameter governing the optimal layout can be identified. To establish this, Rozvany's work on optimization with multiple load cases (Rozvany et al 2014) and the superposition method of Rozvany and Hill (1978) will be used. Figure 1a shows a graphical depiction of the load cases in (2a-2c).…”

Section: Parameter Governing the Optimal Layout R Vhmentioning

confidence: 99%

“…However, this approach requires there to be 2 n load cases, with n being a positive integer. Following Rozvany et al (2014), a fourth, dummy load case p 4 can be introduced, comprising vertical loads V − V . According to Property 3 in Rozvany et al (2014), since V > 0, the optimized result for the problems shown in Fig.…”

Section: Parameter Governing the Optimal Layout R Vhmentioning

confidence: 99%

Layout optimization of building frames subject to gravity and lateral load cases

Tyas

2019

In this study, the optimal layout of the principal structural members forming a building frame are sought, considering both gravity and lateral loads. The plastic design layout optimization formulation is used, considering the multiple load cases arising from the requirements of a well-known structural design code. The superposition approach is shown to be applicable to the three primary load case problems involved. It is found that the optimal layouts identified differ from those obtained when bracing is sought for a pre-existing frame, already designed to resist gravity loads. A significant finding is that a parameter related to the difference in vertical and lateral loads to be applied in the applicable load cases is a key factor determining the optimal layout of frame members. Since applicable load cases are design code dependent, this also indicates that optimal layout will be strongly influenced by choice of design code. Simple benchmark problems and a practical building design example are used to illustrate the concepts explored.

“…This is because plastic yielding of members can occur, allowing forces within the structure to redistribute as necessary. Theoretical issues associated with the plastic multiple load case formulation are considered in more depth by Rozvany et al (2014).…”

Section: Basic Formulationmentioning

confidence: 99%

Application of layout optimization to the design of additively manufactured metallic components

Todd

Derguti

2016

Additive manufacturing ('3D printing') techniques provide engineers with unprecedented design freedoms, opening up the possibility for stronger and lighter component designs. In this paper 'layout optimization' is used to provide a reference volume and to identify potential design topologies for a given component, providing a useful alternative to continuum based topology optimization approaches (which normally require labour intensive post-processing in order to realise a practical component). Here simple rules are used to automatically transform a line structure layout into a 3D continuum. Two examples are considered: (i) a simple beam component subject to three-point bending; (ii) a more complex air-brake hinge component, designed for the Bloodhound supersonic car. These components were successfully additively manufactured using titanium Ti-6Al-4V, using the Electron Beam Melting (EBM) process. Also, to verify the efficacy of the process and the mechanical performance of the fabricated specimens, a total of 12 beam samples were load tested to failure, demonstrating that the target design load could successfully be met.