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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Analysis and Development of Finite Element Methods for the Study of Nonlinear Thermomechanical Behavior of Structural Components

Underintegrated methods are investigated with respect to their stability and convergence properties. The focus was on identifying regions where they work and regions where techniques such as hourglass viscosity and hourglass control can be used. Results obtained show that underintegrated methods typically lead to finite element stiffness with spurious modes in the solution. However, problems exist (scalar elliptic boundary value problems) where underintegrated with hourglass control yield convergent solutions. Also, stress averaging in underintegrated stiffness calculations does not necessarily lead to stable or convergent stress states.

Oden, J. Tinsley↗
NASA NTRS1994

Analysis and control of hourglass instabilities in underintegrated linear and nonlinear elasticity

Methods are described to identify and correct a bad finite element approximation of the governing operator obtained when under-integration is used in numerical code for several model problems: the Poisson problem, the linear elasticity problem, and for problems in the nonlinear theory of elasticity. For each of these problems, the reason for the occurrence of instabilities is given, a way to control or eliminate them is presented, and theorems of existence, uniqueness, and convergence for the given methods are established. Finally, numerical results are included which illustrate the theory.

Jacquotte, Olivier P.↗
NASA NTRS1984

Analysis of hourglass instabilities and control in underintegrated finite element methods

Belytschko et al. (1981, 1984) has developed stabilization methods for the treatment of underintegrated FEM problems; these methods involve the computation of an underintegrated stiffness matrix, which is rank-deficient, and the addition of a stabilization matrix which effectively eliminates the spurious modes. An attempt is presently made to give this a priori stabilization method a mathematical means of support. Attention is also given to an a posteriority stabilization method for hourglass control, in which an approximate solution of the underintegrated system is obtained and then subjected to a special projection in order to eliminate the hourglass modes. A proof is obtained for the convergence of this stabilized underintegrated approximation to the exact solution of a model problem at almost the same rate (as the mesh is refined) as the fully integrated solutions.

Jacquotte, O.-P.↗
NASA NTRS1973

High temperature, low cycle fatigue of copper-base alloys in argon. Part 3: Zirconium-copper; thermal-mechanical strain cycling, hold-time and notch fatigue results

The low-cycle fatigue characteristics of smooth bar and notched bar specimens (hourglass shape) of zirconium-copper, 1/2 Hard, material (R-2 Series) were evaluated at room temperature in axial strain control. Over the fatigue life range from about 300 to 3000 cycles the ratio of fatigue life for smooth bar to fatigue life for notched bar remained constant at a value of about 6.0. Some additional hold-time data for the R-2 alloy tested in argon at 538 C are reported. An analysis of the relaxation data obtained in these hold-time tests is also reported and it is shown that these data yield a fairly consistent correlation in terms of instantaneous stress rate divided by instantaneous stress. Two thermal-mechanical strain cycling tests were also performed using a cyclic frequency of 4.5 cycles per hour and a temperature cycling interval from 260 to 538 C. The fatigue life values in these tests were noticeably lower than that observed in isothermal tests at 538 C.

Conway, J. B.↗