An analytical solution for shape-memory-polymer Euler–Bernoulli beams under bending

• Presenting efficient and accurate analytical expressions for deflection and forces of a shape memory polymer (SMP) beam.
• Employing Euler–Bernoulli beam theory in a thermomechanical SMP cycle.
• Investigating the effects of changing any of the material or geometrical parameters on smart structures consisting of SMP beams.
• This solution is useful in SMP structures design and optimization (e.g., actuators made of SMP beams) where a large number of simulations is required.

The purpose of this paper is to present efficient and accurate analytical expressions for deflection of a shape memory polymer (SMP) beam employing Euler–Bernoulli beam theory in a thermomechanical SMP cycle. Material behavior is considered using a recently 3D thermodynamically consistent constitutive model available in literature. In different steps of an SMP thermomechanical cycle, closed form expressions for internal variables variations, stresses and beam curvature distribution are presented. We show that during the cooling process, stored strains evolve to fix the temporary shape and then during the heating process they relax to recover the permanent shape. Effects of applying external loadings (mechanical constraints) on the SMP beam response for different boundary conditions are also investigated. The proposed analytical solution can be used as an efficient tool for investigating the effects of changing any of the material or geometrical parameters on smart structures consisting of SMP beams. This solution is useful in SMP structures design and optimization (e.g., actuators made of SMP beams) where a large number of simulations is required.