Finite-Element-Mesh Based Method for Modeling and Optimization of Lattice Structures for Additive Manufacturing

Abstract

A parameterization modeling method based on finite element mesh to create complex large-scale lattice structures for AM is presented, and a corresponding approach for size optimization of lattice structures is also developed. In the modeling method, meshing technique is employed to obtain the meshes and nodes of lattice structures for a given geometry. Then, a parametric description of lattice unit cells based on the element type, element nodes and their connecting relationships is developed. Once the unit cell design is selected, the initial lattice structure can be assembled by the unit cells in each finite element. Furthermore, modification of lattice structures can be operated by moving mesh nodes and changing cross-sectional areas of bars. The graded and non-uniform lattice structures can be constructed easily based on the proposed modeling method. Moreover, a size optimization algorithm based on moving iso-surface threshold (MIST) method is proposed to optimize lattice structures for enhancing the mechanical performance. To demonstrate the effectiveness of the proposed method, numerical examples and experimental testing are presented, and experimental testing shows 11% improved stiffness of the optimized non-uniform lattice structure than uniform one.

Considerations on the Applicability of Test Methods for Mechanical Characterization of Materials Manufactured by FDM

“…In addition, as each bar has a different section as a consequence of the different stress values calculated, the lattice structure cannot be considered as uniform along the piece. Thus, those approaches that estimate the mechanical behavior of cellular structures through the testing of specimens out of the standards and that contain a certain number of unit cells would not be of application in this particular case, as in the works of Chen et al [19], who developed a finite element mesh based method for optimization of lattice structures for AM; Hussein [20], who studied the development of lightweight cellular structures for additive manufacturing with metal; Mahmoud and Elbestawi [21], where lattice structures were fabricated by additive manufacturing in orthopedic implants; Maliaris and Sarafis [22], where lattice structures were modelled using a generative algorithm; Panda [23] and Weeger et al [24], who worked in the design and development of cellular structures for AM; or Vannutelli [25], where the mechanical behavior of lattice structures was analyzed. As Figure 1 exposes, a solid layer by layer configuration represents the most consistent As exposed before, from the point of view of the applicability of the mentioned standards, only a continuous material could be characterized.…”

Analysis of General and Specific Standardization Developments in Additive Manufacturing From a Materials and Technological Approach

“…In many of these works the analysis and the characterization of the tested parts combine the performance of mechanical tests in the laboratory and simulation work supported by the Finite Element Method (FEM). This approach allows to validate the results obtained in the simulations and characterize the mechanical behavior of the parts based on this type of structures [92], [95]- [98].…”

“…Usually, the works developed from these kind of approaches, carry out the corresponding mechanical tests considering either the unit cells or small structures obtained as a sum of a certain number of them, but without referring the study to any testing standards and without using the defined specimens in them. The works developed by Chen et al [92] and Hussein et al [93] illustrate the preparation of compression tests on cellular structures. In both cases, compression tests are carried out on the pieces considered without referring them to any testing standard and using own designed specimens, not standardized ones.…”

Optimization Methodology for Additive Manufacturing of Customized Parts by Fused Deposition Modeling (FDM). Application to a Shoe Heel

“…Further studies are developed in previous works to determine the dimensional tolerance to be applied on the nominal diameter of each bar [ 28 ]. Moreover, a uniform repetition pattern is defined throughout the heel’s infill and a size optimization is done to each bar of the lattice structure [ 43 ].…”