A Simple Potential Energy Formulation for 3D Concrete Printed Structures Considering the Shear Effects in the Build-Direction (2023-10)¶

Extrusion-based 3D concrete printing (3DCP) eliminates the need for traditional casting by precisely depositing predetermined volumes of material in subsequent layers using a computer-controlled positioning method. The mechanical response of the layered 3DCP structures from its fresh stages is dependent on several factors including its composition, geometrical flaws, gravity effect, and external disturbance. In the current work, a theoretical formulation has been established considering the shear effects along the build direction. Accordingly, the elastic strain energy and the work done by external forces are derived to establish the potential energy. For simple cases, when the deflection only varies with the vertical direction, the formulation converges to Euler–Bernoulli and Timoshenko beam theory in the absence and presence of shear forces. Finally, making use of simple kinematic admissible functions for deflection and the angle of rotation, the Rayleigh–Ritz method is used to estimate primary variables based on the principle of minimum potential energy.