Enforcing a Force–Displacement Curve of a Nonlinear Structure Using Topology Optimization with Slope Constraints

Abstract

The objective of this study is to develop an optimization methodology to find a layout that traces a prescribed force–displacement curve through a topology optimization approach. To this end, we propose an objective function to minimize the difference between a prescribed force–displacement curve and the curve calculated at each iteration of the optimization process. Slope constraints are introduced to solve issues encountered when using a small number of target points. In addition, a projection filter is employed to suppress the gray region observed between the solid and void regions, which generally occurs when using a density-based filter. A recently proposed energy interpolation scheme is implemented to stabilize the instability in the nonlinear analysis, which generally results from excessive distortion in the void region when the structure is modeled on a fixed mesh in the topology optimization process. To validate the outlined methodology, several case studies with different types of nonlinearity and structural features of the obtained layouts are investigated.

Topology and Parametric Optimization-Based Design Processes for Lightweight Structures

“…The mass reduction here of the Hollow Plate, L-Bracket, and MBB-Beam were 96.9%, 97.3%, and 99.1%, respectively. In addition, the highest mass reduction in the PO workflow could be achieved at process (7) with 95%, 93.4%, and 97.7% mass saving in the three cases. Finally, the dominant process in the TO workflow was process (3) with 74.1%, 62.5%, and 88.8% mass reduction.…”

“…A plethora of research papers focused on either development of new approaches or improvement of the existing optimization methods [7,8]. However, there is limited literature that compares the aforementioned optimization methods or possible combinations of them with respect to their results and optimization time [9,10].…”

The periodically extended stiffness nonlinear energy sink

“…The desired stiffness was obtained by 3D-printing or CNC-machining this profile with a shape that approximately corresponds to the elastic potential energy of the proposed stiffness characteristic. Others have proposed a topology optimized 3D-printed beam, but have only realized slightly hardening spring characteristics [31].…”

Design of composite structures with programmable elastic responses under finite deformations

“…As a powerful computational design methodology, topology optimization has demonstrated its great po-optimization has been adopted in many studies to design novel microstructures with engineered properties, such as negative Poisson's ratio [1,2], negative thermal expansion coefficient [14], tunable elastic modulus [7,8] and stress-strain relations [1,2], photonic and phononic bandgap [15,16], and improved piezoelectric properties [17]. At the structure level, topology optimization has been adopted to program unconventional force-displacement responses, including programming the snap-through [18] and hardening/softening responses of slender structures [19] and controlling the force-displacement path of compliant mechanisms [20].…”