Finite Element Analysis of Shaped Front Endplates for the BaBar Drift Chamber

This note summarizes results from a preliminary stress analysis of several shaped driftchamber endplates using the PC-based finite-element-analysis program ALGOR. We infer from evidence presented below that both the stresses and displacements in thin shaped endplates under uniform wire load scale as 1/thickness. A rough understanding is that the stresses are primarily tension and compression in the shaped structures (compared to primarily bending in a flat endplate). Then for a given force and maximum radius the stress varies as force/area = force/(2πrt) ∝ 1/t. (Whereas in a flat endplate the bending stresses vary as 1/t and displacements as 1/t.) Similar conclusions were reached in a previous study by Bénichou et al., Nucl. Instr. and Meth. 217, 163 (1983). The material was taken as aluminum, with no downrating for holes. About 15% of the endplate volume is lost to holes, so the modulus should be downrated for at least a factor of 0.85 for aluminum. The thermoplastic carbon fiber under consideration by BaBar has a modulus about 0.7 that of aluminum, and must be downrated by another factor of 0.7 due to the holes, according to studies at McGill. The stresses are unaffected by these adjustments in the modulus, but displacements vary inversely with the modulus. Thus the displacements shown in the figures below should be scaled by