Efficient size and shape optimization of truss structures subject to stress and local buckling constraints using sequential linear programming

Abstract

The advance in digital fabrication technologies and additive manufacturing allows for the fabrication of complex truss structure designs but at the same time posing challenging structural optimization problems to capitalize on this new design freedom. In response to this, an iterative approach in which Sequential Linear Programming (SLP) is used to simultaneously solve a size and shape optimization sub-problem subject to local stress and Euler buckling constraints is proposed in this work. To accomplish this, a first order Taylor expansion for the nodal movement and the buckling constraint is derived to conform to the SLP problem formulation. At each iteration a post-processing step is initiated to map a design vector to the exact buckling constraint boundary in order to facilitate the overall efficiency. The method is verified against an exact non-linear optimization problem formulation on a range of benchmark examples obtained from the literature. The results show that the proposed method produces optimized designs that are either close or identical to the solutions obtained by the non-linear problem formulation while significantly decreasing the computational time. This enables more efficient size and shape optimization of truss structures considering practical engineering constraints.

Truss geometry and topology optimization with global stability constraints

“…Finally, we note that there can be seen some degree of resemblance of the optimal designs for the L-shaped problem in Fig. 1e to the solutions obtained by Schwarz et al (2018), Descamps and Coelho (2014), and Ohsaki and Hayashi (2017), where solutions are reported for geometry and topology optimization problems, but where other types of stability constraints are employed.…”

Design of Structures That Adapt to Loads through Large Shape Changes

“…Therefore, definition of limits and the initial configuration for the nodal position is critical. The quality of the solution can be evaluated through comparison against other methods for example those based on linearization (Pedersen, 1973;Schwarz, et al, 2018) or those that include analytical sensitivity (Nocedal & Wright, 1999) (e.g. jacobian and hessian).…”

“…elements with infinitely small cross-section. The search space of the optimization problem stated in Equation 4to (10) is continuous but not convex because the nodal coordinates are part of the design variables and due to the element buckling constraint (Schwarz, et al, 2018). This problem was solved through sequential quadratic programming (SQP) (Boogs & Tolle, 1995).…”

Optimization-driven conceptual design of truss structures in a parametric modelling environment

“…The use of NLP optimization not only allows rationalization of structural forms, but also provides a means of addressing various practical constraints that are non-linear in form, such as Euler buckling. This can be incorporated in Stage 2 by adding the following constraint (after [41,42]):…”