### TABLE I. Fatigue-Crack Growth DKth Thresholds for Thin-Walled Superelastic Nitinol Tube as a Function of Load Ratio, R

2007

### Table 1 Empirical convergence rates for u, v, p, and X in the discrete L1 and L2 norms at time t = 0.4. In these computations, the stiffness of the elastic fibers comprising the shell tapers to zero at the edges of the structure, so that there is a continuous transition in material properties at the fluid-structure interface. Convergence rates are obtained via equations (37) and (38).

in rates

"... In PAGE 19: ... As long as the structure does not become too distorted, the resulting Cartesian elastic force density, f, will remain a continuous function of x. Table1 summarizes the empirical convergence rates in the discrete L1 and L2 norms observed for u, v, p, and X at time t = 0.4.... In PAGE 21: ... This is likely due to inadequate resolution of the flow for N = 128 in the vicinity of narrow bands of high vorticity that form near the fluid-structure interface. As shown in Table1 , when we employ delta functions which satisfy four mo- ment conditions (i.e.... ..."

### Table 2 Empirical convergence rates for u, v, p, and X in the discrete L1 and L2 norms at time t = 0.4. In these computations, the stiffness of the elastic fibers comprising the shell is constant throughout the structure, so that there is a sharp transition in material properties at the fluid-structure interface. Convergence rates are obtained via equations (37) and (38).

in rates

"... In PAGE 22: ...08/N. For this particular choice of material properties, Table2 summarizes the em- pirical L1 and L2 norm convergence rates observed for u, v, p, and X at t = 0.4.... ..."

### Table 3: Pareto solutions

1997

"... In PAGE 6: ... It must be emphasize that as formulated and solved here, at least the first example is rather simple, but the goal is to show that even in such simple design models, one can derive the benefit of very rich strategic decision- making interpretations between the players. 3 Design of a Thin-Walled Pressure Vessel In this simple example, consider the design of a thin-walled pressure vessel which has hemispherical ends as shown in Figure 3 (see Table3 for the nomenclature for this example). This case-study is derived from a similar example in Karandikar and Mistree [13] where it was used to illustrate a decision-support formulation.... ..."

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### TABLE II. Equivalent Fracture Toughness Values for Thin-Walled Superelastic Nitinol Tube Computed From Maximum Strain-Energy Release Rates to Compensate for Angled Crack Growth in the Circumferential Direction

2007

### Table 2. The results of the variable section solutions

in COMPUTATIONAL TOOLS FOR SEMI-ANALYTICAL FINITE ELEMENT STABILITY ANALYSIS OF THIN-WALLED STRUCTURES

"... In PAGE 11: ...The numerical results show the good agreement between the proposed model and the results obtained from the classical theory and solutions by a shell FE model ( Table2 ). Therefore, the proposed models are actual in the range of thin cross-sectional walls and fill the gap between the theory of thin-walled beams and shells.... ..."

### Table 2. Examples of tubes and computed parameters, including critical and characteristic speeds.

"... In PAGE 7: ...ation used in the laboratory at Caltech is shown in Fig. 5. The tube is made of up of three sections 2.3 m long, each with the properties shown in the second column of Table2 . The tube was instrumented with piezoelectric pressure transducers and bonded strain gages (oriented to measure the hoop component) [30].... In PAGE 8: ...5 mm thick, 40 mm diameter aluminum tube specimen that was 1.5 m long (column 1 in Table2 ). Detonations were initiated in a separate thick-wall section 1.... In PAGE 12: ...(b) (c) Figure 12. Thin-wall (first column of Table2 ) tubes with pre-existing flaws, rupture due to propagating detonations [59].... In PAGE 12: ... Figure 13. Crack opening and propagation in thin-wall (first column of Table2 ) tube under torsion with a pre-existing flaw and detonation loading [52]. 12 Copyright c... In PAGE 15: ...DT near a closed end, for example, as shown in Fig. 15. Figure 15. Plastic deformation of 15% produced in a thin-wall tube (col- umn 3 of Table2 ) of mild steel by DDT next to closed end located at the right-hand side. The peak pressure measured at the end was ap- proximately 500 bar, twice the computed value for a reflected CJ detona- tion [77].... ..."

### Table 4: Convergence results for die-flexure problem.

2001

"... In PAGE 46: ... In that case, we are hard pressed to find a suitable preconditioner. The first row of Table4 corresponds to the flow-only QlPO case. ILUT(l.... In PAGE 47: ...election, i.e., using per- turbations to lower the condition number and increasing the level of fill to improve convergence. In row 5 of Table4 we again employ the QlPO element but include the entire fluid-structural interaction problem. The number of unknowns in this case was approximately 80,000.... ..."

### Table 1. Vessel design problem

2005

"... In PAGE 5: ...etween 0.9 and 0.4. The numerical results for the engineering problems de- scribed in [3] are presented in Table1 , Table 2, Table 3 and Table 4. Numerical comparison between a particle swarm penalty approach and genetic algorithms is made in [3] and we chose to report only the numerical results related to therein proposed particle swarm algorithm.... ..."

### TABLE I Scaling Constants in the Paris Law [Eq. (1)] and Modified Paris Law [Eq. (2)] for Nitinol Thin-Walled Tube Samples Load Ratio, RmC(m/cycle/(MPa Hm)m) npC0 (m/cycle/(MPa Hm)m)

Cited by 1