## What is/are Graded Lattice?

Graded Lattice - With this new algorithm modular lattices are counted up to 30 elements, semimodular lattices up to 25 elements, graded lattices up to 21 elements, and geometric lattices up to 34 elements.^{[1]}The upgraded lattice will use as many NSLS-II installed magnets as possible, including 30 dipoles, which will create a triple bend achromat configuration.

^{[2]}To realize topologically-optimized structures filled with functionally-graded lattices, Helmholtz PDE-filter with a variable radius is applied on the density field in Solid Isotropic Material with Penalization (SIMP) method.

^{[3]}

## Functionally Graded Lattice

Compared with uniform structures, functionally graded lattice structures can control mechanical properties through varying structure and volume fraction.^{[1]}Parameter and functionally graded lattice optimization were employed to reduce mass within deflection criteria.

^{[2]}TiNi functionally graded lattice structure (FGLS) is bio-inspired by bone architecture and processed by AM.

^{[3]}Composites reinforced by vertically functionally graded lattice structures have a significantly lower reinforcing ratio while exhibiting obviously higher normalized ductility.

^{[4]}Compared with the uniform lattice structures, the functionally graded lattice structures showed better performance in terms of initial peak strength, compressive modulus and energy absorption.

^{[5]}Human bones are biological examples of functionally graded lattice capable to withstand large in vivo loading and allowing optimal stress distribution.

^{[6]}Where certain domains of the part require denser infill compared to other domains, the functionally graded lattice structure allows for further part optimization.

^{[7]}, topology-optimised materials and functionally graded lattice materials (FGLMs), can be well fabricated with the assistance of additive manufacturing (AM).

^{[8]}The size optimisation results in a functionally graded lattice whereby lattice truss diameters become the design variables.

^{[9]}Additive Manufacturing is enabling the casting of complex geometries directly from digital design data, including 3D-scanned and reverse-engineered structures and even functionally graded lattices.

^{[10]}The wireframe structure is easily transferred into one-dimensional beam elements for microscale optimizations to obtain a functionally graded lattice material.

^{[11]}To solve the problems of uneven stress distribution, stress concentration, and local failure, a parametric design method of functionally graded lattice structure based on stress distribution law is proposed.

^{[12]}This paper aims to evaluate the potential use of an innovative functionally graded lattice-filled composite beam composed of axial and radial graded three-dimensional lattice cores.

^{[13]}Potential application for functionally graded lattice structures is presented.

^{[14]}Functionally graded lattice structures (FGLs) are structures that are designed using lattices with a varying distribution of porosity by virtue of varying the volume fractions of each unit cell in the 3D design domain.

^{[15]}Functionally graded lattice (FGL) structures were produced by selective laser melting (SLM) method, representing an increasingly growing additive manufacturing engineering area introduced in material engineering.

^{[16]}Owing to the advancement of additive manufacturing (AM), the development of design methods for additively manufactured lattice structures has extensively progressed, especially for functionally graded lattice structures (FGLS).

^{[17]}This new method of generating functionally graded lattices is shown both numerically and experimentally to be capable of generating lattice structures with greatly improved stiffness and strength when compared to lattice structures with a uniform lattice infill.

^{[18]}The gradient theory of piezoelectricity is developed for 3D analyses of QDs with the functionally graded lattice mismatch between the QD and the matrix.

^{[19]}

## graded lattice structure

Compared with uniform structures, functionally graded lattice structures can control mechanical properties through varying structure and volume fraction.^{[1]}TiNi functionally graded lattice structure (FGLS) is bio-inspired by bone architecture and processed by AM.

^{[2]}Three types of lattice structures composed of body-centred cubic (BCC) unit cells were studied, including uniform lattice structures, uni-directionally graded lattice structures and bi-directionally graded structures.

^{[3]}Laser powder bed fusion (LPBF) additive manufacturing of pure tantalum and their graded lattice structures was systematically investigated, with emphasis on their microstructure evolution, phase formation, surface energy and biological properties in comparison with conventionally forged pure Ta.

^{[4]}Composites reinforced by vertically functionally graded lattice structures have a significantly lower reinforcing ratio while exhibiting obviously higher normalized ductility.

^{[5]}Compared with the uniform lattice structures, the functionally graded lattice structures showed better performance in terms of initial peak strength, compressive modulus and energy absorption.

^{[6]}Graded lattice structures (GLSs) have drawn much attention in engineering and biological areas due to the enhanced mechanical properties and energy absorption capacity that benefited from the graded porosity design.

^{[7]}Graded lattice structures (GLSs) have drawn much attention in engineering and biological areas due to the enhanced mechanical properties and energy absorption capacity that benefit from the graded design.

^{[8]}Where certain domains of the part require denser infill compared to other domains, the functionally graded lattice structure allows for further part optimization.

^{[9]}To reduce the stress concentration and ensure structural safety for lattice structure designs, in this paper, a new optimization framework is developed for the optimal design of graded lattice structures, innovatively integrating fillet designs as well as yield and buckling constraints.

^{[10]}This paper proposes a new design of lightweight-graded lattice structures to replace the internal solid volume of the turbine blade to increase its endurance of high thermal stresses effects.

^{[11]}Taking advantage of multi-cell tubes and lattice structures on improving crashworthiness performances, a novel multi-cell thin-walled tube filled with uniform and graded lattice structures is explored in this paper.

^{[12]}By changing the unit cell size and arrangement, five different graded lattice structures with various relative densities made of soft and hard materials are numerically investigated.

^{[13]}To solve the problems of uneven stress distribution, stress concentration, and local failure, a parametric design method of functionally graded lattice structure based on stress distribution law is proposed.

^{[14]}Potential application for functionally graded lattice structures is presented.

^{[15]}Functionally graded lattice structures (FGLs) are structures that are designed using lattices with a varying distribution of porosity by virtue of varying the volume fractions of each unit cell in the 3D design domain.

^{[16]}Porosity-graded lattice structures are used in bone implants to mimic natural bone properties.

^{[17]}In this work, a novel methodology is proposed to design graded lattice structure through topology optimization under stress constraint, in order to generate lightweight lattice structure design with predictable yield performance.

^{[18]}Graded lattice structure optimization is utilized to design the support structure due to the open-celled and self-supporting nature of periodic lattice structure.

^{[19]}The graded lattice structures have advantages in optimizing structure.

^{[20]}Owing to the advancement of additive manufacturing (AM), the development of design methods for additively manufactured lattice structures has extensively progressed, especially for functionally graded lattice structures (FGLS).

^{[21]}

## graded lattice material

Graded lattice materials, named metamorphic (MM), allow bandgap engineering to optimize the solar spectrum match.^{[1]}, topology-optimised materials and functionally graded lattice materials (FGLMs), can be well fabricated with the assistance of additive manufacturing (AM).

^{[2]}The wireframe structure is easily transferred into one-dimensional beam elements for microscale optimizations to obtain a functionally graded lattice material.

^{[3]}