Experimental study and finite deformation analysis of the sagging behavior of a polymer sheet

The deformation of a heated plastic sheet clamped on only two sides subject to sagging under its own weight was modeled as a membrane or cable undergoing a finite deformation and large rotation. A one-dimensional formulation which assumed that the plane sections remain plane and perpendicular to the center-line, served as a starting point to describe the deformation of a clamped sheet. A membrane approximation which neglects the moment and reactive shear force was used in the equilibrium equations. The membrane equations were made time dependent to reflect the slow time-dependent nature of sheet sag. A multi-element Maxwell constitutive model was used in conjunction with the time dependent membrane formulation (rate equations) to describe the sheet sag. The effect of temperature expansion and contraction was also included. The formulation yielded deflections which compared reasonably well with the experimental data.