Isogeometric configuration design optimization of shape memory polymer curved beam structures for extremal negative Poisson’s ratio

Using a continuum-based design sensitivity analysis (DSA) method, a configuration design optimization method is developed for curved Kirchhoff beams with shape memory polymers (SMP), from which we systematically synthesize lattice structures achieving target negative Poisson’s ratio. A SMP phenomeno...

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Bibliographic Details
Published inStructural and multidisciplinary optimization Vol. 58; no. 5; pp. 1861 - 1883
Main Authors Choi, Myung-Jin, Cho, Seonho
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2018
Springer Nature B.V
Subjects
Beam theory (structures)
Boundary conditions
Computational Mathematics and Numerical Analysis
Configuration management
Configurations
Constitutive models
Curved beams
Deformation
Design analysis
Design optimization
Engineering
Engineering Design
Finite difference method
Nonlinear analysis
Poisson's ratio
Research Paper
Sensitivity analysis
Shape memory
Synthesis
Theoretical and Applied Mechanics
Isogeometric analysis
Negative Poisson’s ratio
Displacement loading
Geometric nonlinearity
Shape memory polymer
Configuration design sensitivity
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Summary:Using a continuum-based design sensitivity analysis (DSA) method, a configuration design optimization method is developed for curved Kirchhoff beams with shape memory polymers (SMP), from which we systematically synthesize lattice structures achieving target negative Poisson’s ratio. A SMP phenomenological constitutive model for small strains is utilized. A Jaumann strain, based on the geometrically exact beam theory, is additively decomposed into elastic, stored, and thermal parts. Non-homogeneous displacement boundary conditions are employed to impose mechanical loadings. At each equilibrium configuration, an additional nonlinear analysis is performed to calculate the Poisson’s ratio and its design sensitivity of the SMP material. The design objectives are twofold: for purely elastic materials, lattice structures are designed to achieve prescribed Poisson’s ratios under finite compressive deformations. Also, SMP-based lattice structures are synthesized to possess target Poisson’s ratios in specified temperature ranges. The analytical design sensitivity of the Poisson’s ratio is verified through comparison with finite difference sensitivity. Several configuration design optimization examples are demonstrated.
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-018-2088-y