An analytical exact, locking free element formulation for thin-walled composite Timoshenko beams

Spatial truss structures represent a robust, cost-effective, and efficient lightweight design, especially when isotropic materials are substituted with lightweight materials such as composites. During early design phases, truss structures are often subject to optimisations. In order to achieve this in an efficient manner, it is essential to employ a precise yet cost-effective computational model. The most common methodology for the analysis of spatial truss structures employs hinged joints in conjunction with struts that are only subject to tension or compression. However, this approach does not account for the bending and coupling effects inherent to struts manufactured from composite materials. In particular, when employing asymmetric laminates, these effects can no longer be ignored. In order to incorporate these effects, it is common practice to use Finite Element Analysis tools. Particularly for large spatial truss structures comprising struts with slender and thin-walled cross-sections, a large number of solid or shell elements is required, which results in time-consuming simulations. This contribution presents a fully analytical thin-walled composite beam element, applicable to an arbitrarily shaped, closed cross-section. The beam model incorporates two distinct composite material models, namely the Classical Laminate Plate Theory and the First Order Shear Deformation Theory. Moreover, it is capable of simulating asymmetric laminates and modelling the coupling effects within these laminates. Utilising the exact third-order solution of a composite Timoshenko-Ehrenfest beam enables the locking-free representation of an individual strut with a single beam element. In comparison to the conventional shell / solid Finite Element Analysis, this approach results in a substantial reduction in the number of degrees of freedom, by a factor of several orders of magnitude. As a result, the required computational time is significantly reduced. In the case of a single strut, the computational time is reduced by a factor between 160 and 430. For an exemplary truss structure comprising 64 struts, a reduction in computational time of approximately 100 000 times is reached. The numerical comparisons presented in this contribution demonstrate that the model is highly accurate, particularly for tubular and elliptical cross-sections including symmetric and asymmetric laminates.