TY - JOUR

T1 - An efficient semi-analytical framework to tailor snap-through loads in bistable variable stiffness laminates

AU - Haldar, Ayan

AU - Groh, R. M.J.

AU - Jansen, Eelco

AU - Weaver, Paul M.

AU - Rolfes, Raimund

N1 - Funding Information: A. Haldar is grateful to the German Research Foundation (DFG) for funding the research through the International Research and Training Group IRTG 1627 ?Virtual materials and their validation?. A. Haldar would like to thank Dr. A. Pirrera, Senior Lecturer, Bristol Composites Institute (ACCIS), University of Bristol, Bristol for his valuable comments and discussions. R.M.J. Groh is supported by the Royal Academy of Engineering under the Research Fellowship scheme (Grant no. RF\201718\17178). P.M. Weaver wishes to thank the Science Foundation Ireland for funding Varicomp (Grant no.: 15/RP/2773) under its Research Professor scheme.

PY - 2020/6/15

Y1 - 2020/6/15

N2 - Multistable laminates are potential candidates for adaptive structures due to the existence of multiple stable states. Commonly, such bistable shapes are generated from the cool-down process of the unsymmetric laminates from the curing temperature. In this work, we exploit unsymmetric variable stiffness laminates with curvilinear fiber paths to generate similar bistable shapes as unsymmetric cross-ply laminates, but with the possibility to tailor the snap-through loads. Snap-through is a complex phenomenon in that is difficult to characterize using simple analytical models. An accurate yet computationally efficient semi-analytical model is proposed to compute the snap-through forces of bistable variable stiffness (VS) laminates. The differential equations resulting from the compatibility and the in-plane equilibrium equations are solved with negligible numerical error using the Differential Quadrature Method (DQM). As a result, the in-plane stress resultants and the total potential energy is written in terms of curvatures. The out-of-plane displacements are expressed in the form of Legendre polynomials where the unknown coefficients of the displacement function are found using the Rayleigh-Ritz formulation. The calculated snap-through loads are then compared with the Finite Element (FE) results. A parametric study is conducted to explore the tailoring capabilities of VS laminates for snap-through loads.

AB - Multistable laminates are potential candidates for adaptive structures due to the existence of multiple stable states. Commonly, such bistable shapes are generated from the cool-down process of the unsymmetric laminates from the curing temperature. In this work, we exploit unsymmetric variable stiffness laminates with curvilinear fiber paths to generate similar bistable shapes as unsymmetric cross-ply laminates, but with the possibility to tailor the snap-through loads. Snap-through is a complex phenomenon in that is difficult to characterize using simple analytical models. An accurate yet computationally efficient semi-analytical model is proposed to compute the snap-through forces of bistable variable stiffness (VS) laminates. The differential equations resulting from the compatibility and the in-plane equilibrium equations are solved with negligible numerical error using the Differential Quadrature Method (DQM). As a result, the in-plane stress resultants and the total potential energy is written in terms of curvatures. The out-of-plane displacements are expressed in the form of Legendre polynomials where the unknown coefficients of the displacement function are found using the Rayleigh-Ritz formulation. The calculated snap-through loads are then compared with the Finite Element (FE) results. A parametric study is conducted to explore the tailoring capabilities of VS laminates for snap-through loads.

KW - Differential quadrature method

KW - Multistability

KW - Nonlinear plates

KW - Rayleigh Ritz

KW - Residual thermal stresses

KW - Snap-through loads

KW - Variable stiffness composites

UR - http://www.scopus.com/inward/record.url?scp=85083303478&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2020.02.018

DO - 10.1016/j.ijsolstr.2020.02.018

M3 - Article

AN - SCOPUS:85083303478

VL - 195

SP - 91

EP - 107

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

ER -