Physics

Finite element method

Nonlinear system

Shape optimization

Mathematics

Structural engineering

Poisson's equation

Poisson distribution

Operating system

Configuration design

Statistics

Poisson's ratio

Engineering

Mathematical analysis

Beam (structure)

Boundary value problem

Acoustics

Materials science

Sensitivity (control systems)

Electronic engineering

Lattice (music)

Computer science

Quantum mechanics

Structural and Multidisciplinary Optimization

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.

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