Lattice structures have received increasing attention due to their superior specific stiffness and strength. Elastic buckling is one of the main failure mechanisms of lightweight lattice structures, playing a crucial role on their compressive strength. Significant strength improvements can be achieved in the range of low relative density by improving buckling resistance.

We present an effective design approach for improving the critical buckling loads of sandwiched 3D Kagome lattice cores with free-form trusses. In this framework, the shapes of the truss members are characterized by Fourier series (FSs) and implicit surfaces, which guarantees smooth truss shapes and the transitions at truss joints. In the design process, a truncated FS is applied since low-order terms strongly contribute to smooth and slowly-varying shapes while high-order terms mainly formulate undesired local sharp features.



Figure 1. Design methodology of this project.

Using this design method, a free-form truss can be characterized as the radius function in terms of FS coefficients  by

where l is the length of the truss and  is the original diameter of the truss.

Figure 2. Generation of free-form lattice geometries with Fourier series: the free-form 1D columns defined as  with (a)  , (b)  , (c)  ; (d – f) the corresponding 3D Kagome lattice cores with the core height h and internal angle θ.

Numerical designs of both 1D columns and 3D Kagome lattice cores are carried out by using the present approach. The optimized results include trusses with curved and non-uniform sections, presenting significant improvements of their critical buckling loads. In addition, both original and optimized structures of identical masses are fabricated via AM, where the curved shapes of optimized trusses can be precisely captured. Experimental testing is also conducted to evaluate their performance. Both numerical and experimental results demonstrate the effectiveness of the proposed method.

Figure 3. The (a) initial and (b) optimized columns, and the (c) initial and (d) optimized Kagome lattice structures connected to face plates.

Figure 4. Load-displacement graphs of the initial and optimized 1D columns with minimal radius constraint. Two typical buckling modes due to the experimental imperfections of the optimized columns are highlighted.

Figure 5. Load-displacement graphs of the initial and optimized Kagome lattice core structures.

Related publication:

Zhang, L., Feih, S., Daynes, S., Wang, Y., Wang, M. Y., Wei, J., & Lu, W. F. (2018). Buckling optimization of Kagome lattice cores with free-form trusses. Materials & Design. In press.