Optimal positioning of heating lines in a compression molding die using the boundary element method

摘要

A shape optimization problem is formulated to determine the optimal position of heating lines in a compression molding die. The objective of the problem is that the die cavity surface would be maintained by a prescribed uniform temperature. A new boundary integral equation for the sensitivity of the temperature in terms of the hole position is derived using the method of shape design sensitivity analysis. The boundary element method is employed to analyze the temperature and its sensitivity field. The presented sensitivity formulation is incorporated in an optimization routine. To demonstrate a numerical implementation, an example problem arising in thermal design of a compression molding die is dealt with, showing the effectiveness and usefulness of the presented method.