Multiple-point constraint applications for the finite element analysis of shear deformable composite beams – Variational multiscale approach to enforce full composite action

• Layers are connected using multiple-point constraints at the nodes.
• Variational multiscale approach is used to identify the numerical error.
• Full-interaction between the layers could be recovered.
• Numerical error can be represented by using extra fictitious elements and springs.

Composite beams that consist of two or more shear deformable layers find widespread applications in a variety of engineering structures. In the computational modelling of composite beams, the layers can be stacked together and connected conveniently at the nodes by using multiple-point constraints. However, this type of modelling does not inherit the kinematic behaviour of the continuous case and thus full-interaction between the layers cannot be always imposed by applying multiple-point constraints at the nodes. The work herein shows that in multiple-point constraint applications full composite action between the shear deformable layers can be recovered by using the variational multiscale approach. The originality of this study is in the interpretation of the multiple-point constraint application as the solution in a superfluously extended space because of the weakening in the kinematic constraints. It is shown that full composite action between the beam layers can be recovered by excluding the identified fine-scale effect from the solution of the multiple point constraint application. Selected examples illustrate the effects of loading and relative layer stiffness on the numerical error as well as modelling options for fully composite and delaminated beams.