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FEA Puzzler: a Tale of Two Analysts

FEA Puzzler: a Tale of Two Analysts


This FEA puzzler was devised by Barna Szabo of Engineering Software Research and Development, Inc. Prof Szabo will be giving a keynote presentation, “On the Formulation and Application of Design Rules” at the NAFEMS World Congress.The decision to including the FEA puzzler in benchmark was influenced by discussions with the AMWG regarding the competencies a certified PSE analyst should exhibit.

A composite ring was made by joining a stainless steel(ss) and a titanium (Ti) ring. At room temperature (20°C) the rings are stress-free.Two analysts were asked to compute the maximum principal stress (σ1) max when the temperature of the the composite ring is increased to 120°C. They were asked to assume that the two materials are perfectly bonded and the assumptions of the linear theory of elasticity are applicable.The geometric and material parameters are shown in Table 1.

Geometric and Material properties

Table 1: Geometric and Material properties

Analyst A formulated this as a problem of plane stress.He used two quadrilateral elements on a 30-degreesector. The analyst verified his solution by performing a mesh convergence study and reported that the maximum principal stress occurs along the material interface and its value is 22.1 MPa.

Notation

Figure 1: Notation

Analyst B formulated this as an axisymmetric problem.He generated a uniform mesh of 800 nine-node quadrilateral elements. He reported that the maximum principal stress occurs at r = rm, z = t/2 and its value is 52.4 MPa. Relying on his judgment that the mesh was fine enough, he did not perform solution verification.Your supervisor asked you to find out why such a large discrepancy exists between the two results. Having checked the input data, you found no errors.Your supervisor would like to know what the maximum principle stress in the component is. 

Please submit your response to challenge@nafems.org. All correct responses will receive a NAFEMS branded business-cardholder.

The solution will be published in the July edition of benchmark.