A Numerical Solution of the Inverse Problem for Thermoforming Processes Using Finite Element Analysis

Finite element analysis of thermoforming simulation based on isothermal as well as non-isothermal initial conditions has been applied successfully for predicating final thickness distributions. For these simulations, it is assumed that the initial sheet temperature is known and does not change significantly during forming at a rapid stretch rate. For a non-isothermal analysis, the temperature dependent material properties are necessary. In this paper sample results are presented for the so-called inverse thermoforming problem, where an initial temperature distribution is sought numerically that will result in a specific final thickness distribution. Thus, a finite element simulation is combined with an iterative algorithm to obtain inverse solutions for a thermoformed part. In this example, the required initial temperature distributions that result in a uniform final thickness are determined for a thermoformed part. It is shown that the calculated results are quite sensitive to perturbations in the specified initial temperature profile and thus the practical application of optimal temperature distributions may require high precision thermal sensors and controls. This initial temperature distribution can then be used for the determination of desired heating patterns on zone-controlled heaters of a thermoforming machine using transient heat transfer analysis.