Open Access Open Access  Restricted Access Subscription Access

Topology Optimization of Plate Structures with Anisotropic Materials



This work presents a topology optimization method for the design of structures composed exclusively of rectangular plates made of a predetermined, generally anisotropic material. The geometry projection method is employed to map the highlevel geometry and material properties to a fixed grid for the analysis, thus circumventing the need to re-mesh upon each design iteration. We also impose an overlap constraint in the optimization that reduces waste material when fabricating structures by cutting and joining rectangular plates. We demonstrate our method with a numerical example comparing optimal cantilever beam designs obtained using isotropic- and orthotropic-material plates. For this example, we maximize the stiffness of the structure for a fixed amount of material, and we impose a constraint to reduce overlaps between plates. The examples demonstrate the importance of considering material anisotropy in the design of plate structures. Moreover, it is demonstrated that an optimally stiff design for plates made of an isotropic material can exhibit poor performance if the plates are naively replaced with an anisotropic material.


Full Text:



Daniel, I. M. and O. Ishai. 2006. Engineering Mechanics of Composite Materials. Oxford

University Press, New York.

George, M. 2007. “Composites help propel GKN aerospace growth,” Reinforced Plastics, pp. 26-29

Tsai S.W. 1965. “Strength Characteristics of Composite Materials.” Technical report, Philco Corp.

Newport Beach CA.

Groenwold, A. A. and R. T. Haftka. 2006. “Optimization with Non-homogeneous Failure Criteria

like Tsai-Wu for Composite Laminates.” Structural and Multidisciplinary Optimization, 32(3): pp.


Venkataraman, S. and R. T. Haftka. 1999. “Optimization of Composite Panels-A Review.” In

Proceedings-American Society for Composites, pp. 479-488.

Nikbakt, S. et. al, 2019. “A Review on Optimization of Composite Structures Part I: Laminated

Composites.” Composite Structures, 195: pp. 158–185

Jia, H. P., et. al. 2009. “Topology Optimization of Orthotropic Material Structure.” Materials

Science forum, 575-578: pp. 978-989.

Boddeti, N. et. al. 2018. “Simultaneous Digital Design and Additive Manufacture of Structures and

Materials.” Scientific Reports, 8(1): pp. 1-10.

Stegmann, J. and E. Lund. 2005. “Discrete Material Optimization of General Composite Shell

Structures.” International Journal for Numerical Methods in Engineering, 62(14): pp. 2009-2027.

Nomura, T., et. al. 2015. “General Topology Optimization Method with Continuous and Discrete

Orientation Design using Isoparametric Projection.” International Journal for Numerical Methods

in Engineering, 101(8): pp. 571-605.

Zhou, Y. et. al. 2018. “Multi-component Topology and Material Orientation Design of Composite

Structures (MTO-C).” Computer Methods in Applied Mechanics and Engineering, 342: pp. 438-

Wein, F., et. al. 2020. “A Review on Feature-mapping Methods for Structural Optimization.”

Structural and Multidisciplinary Optimization. pp. 1-42.

Smith, H. and J. Norato. 2019. “Geometric Constraints for the Topology Optimization of Structures

Made of Primitives.” SAMPE.

Zhang, S. et. al. 2016. “A Geometry Projection Method for the Topology Optimization of Plate

Structures.” Structural and Multidisciplinary Optimization, 54(5): pp. 1173-1190.

Hoang V. N. and G. W. Jang. 2017. “Topology Optimization Using Moving Morphable Bars for

Versatile Thickness Control.” Computer Methods in Applied Mechanics and Engineering, 317: pp.


Zhang S. and J. A. Norato. 2017. “Optimal Design of Panel Reinforcements with Ribs Made of

Plates.” Journal of Mechanical Design, 139(8).

Zhang W., et. al. 2018. “A Moving Morphable Component Based Topology Optimization

Approach for Rib-stiffened Structures Considering Buckling Constraints.” Journal of Mechanical

Design, 140(11).

Norato, J. A. et. al. 2015. “A Geometry Projection Method for Continuum-based Topology

Optimization with Discrete Elements.” Computer Methods in Applied Mechanics and Engineering,

: pp. 306-327.

Guo, X. et. al. 2014. “Doing Topology Optimization Explicitly and Geometrically a New Moving

Morphable Components Based Framework.” Journal of Applied Mechanics, 81(8): pp. 081009.

Smith, H. and J. Norato. 2021. “Topology Optimization with Discrete Geometric Components

Made of Composite Materials.” Computer Methods in Applied Mechanics and Engineering. 376:

pp. 113582.

Smith, H. and J. Norato. 2020. “A Topology Optimization Method for the Design of Orthotropic

Plate Structures.” International Design Engineering Technical Conferences and Computers and

Information in Engineering Conference. Vol. 84003. American Society of Mechanical Engineers.

Smith, H. and J. Norato. 2021. “Topology Optimization of Plate Structures made with Orthotropic

Materials.” (in progress).


  • There are currently no refbacks.