Date of Award

Spring 1995

Document Type

Thesis - Restricted

Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Weber, Robert C.

Second Advisor

Nigro, Nicholas J.

Third Advisor

Wenzel, Thomas H.


The criteria necessary to achieve convergence for a finite-element model of a ("C" shaped) Bourdon tube using readily available commercial software (with commonly found elements) is presented here along with the tip deflection results. In addition, the effects of wall thickness, wall thickness variations within the tube, Poisson's ratio and the linearity of tip deflection vs. pressure were also studied. A comparison is made between 6 DOF (Degree of Freedom) quadrilateral shell (4 node thin/thick & 8 node thin-shell) and solid (8/20 node 3 DOF brick & 4 node 3/6 DOF tetrahedral) elements. The primary focus is on 4 node thin-shell and 8 node solid elements utilizing the COSMOS/M (from Structural Research & Analysis Corp., Santa Monica, California) finite-element analysis software package. No customized programming was needed to build and run these models. Macros, however, were easily written through the software to aid in the repetitive portions of the model building. Tip deflections using 4 node shell elements were shown to be less than the experimental values for thin-walled tubes (5.0% error) and greater than the experimental values for the thick-walled tubes (17.4% error). The use of thick-shell elements increased the tip deflection by 13.2% for thick-walled tubes. The use of higher order 8 node elements increased the deflections by 6.5% for thin- and 17.8% for thick-walled tubes. Similar results to the 4 node shell elements were experienced with 8 node solid brick elements with errors being 4.4% and 19.3% for thin- and thick-walled tubes, respectively. The use of a higher order 20 node brick element increased deflections by 4.0% for thin- and 5.5% for thick-walled tubes. Six DOF solid elements are not readily available. However, 3 and 6 DOF 4 node tetrahedral elements were available for comparison. As expected the 3 DOF tetrahedrons proved to be a very stiff element, under-reporting the deflections by about 60% to 70% for both cases. The 6 DOF tetrahedrons still under-reported the deflections for both cases, but improved the error to 25.4% for the thin- and 10.0% for the thick-walled tubes. The use of higher order elements was not investigated for 6 DOF solid elements. Regardless of the type of element used, maximum aspect ratios of 4 or 5: 1 (as recommended by most software vendors) showed the best performance for the number of elements used and the time it took to run an analysis.



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