J.M. Kennedy

Hourglass control in linear and nonlinear problems

Abstract Mesh stabilization techniques for controlling the hourglass modes in under-integrated hexahedral and quadrilateral elements are described. It is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly. It is also shown that this leads to an hourglass control that satisfies the patch test. The nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed. Finally, effective means of implementing these hourglass procedure in computer codes are described. Applications to both the Laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered.

COMPUTER MODELS FOR SUBASSEMBLY SIMULATION

Abstract Two-dimensional finite element models for the treatment of the nonlinear, transient response of fluids and structures are described. The fluid description is quasi-Eulerian, so that the mesh can move independently of the material and it includes a new finite element upwinding scheme. The structural description is based on a corotational formulation in which the coordinate system is embedded in the elements, and which is applicable to arbitrarily large rotations. The interface between the fluid and structure permits relative sliding, but because of the quasi-Eulerian fluid description the nodes of the fluid and structure can be allowed to remain contiguous. Modelling procedures for treating the various aspects of subassemblies, such as the narrow fluid channels, the fuel bundles which are immersed in the coolant, and the axial flow, are developed. Calculations are made for a symmetric seven-subassembly cluster and compared to experimental results. In addition, the application to a 19-subassembly cluster is described.

Finite element methods with user-controlled meshes for fluid-structure interaction

Abstract A quasi-Eulerian finite element formulation for the analysis of transients in a fluid with a pressurized bubble is developed in both two and three dimensions. In these methods the mesh can be programmed to move independent of the material, so that the method lends itself well to the treatment of fluid-structure problems. Time integration is performed by an explicit method, and one point quadrature is used in the fluid elements. To eliminate hourglass modes, an hourglass control which is orthogonal to straining and rigid body modes is used. Several examples are described.

Finite element analysis on the connection machine

Abstract This paper describes the adaptation of a finite element program with explicit time integration to a massively parallel SIMD computer, the CONNECTION machine. The adaptation required the development of a new procedure, called an ‘exchange’, which consists of an exchange of nodal forces at each time step to replace the standard gather and assembly. In addition, the data was reconfigured so that all nodal variables associated with an element are stored in a processor along with other element data. The architectural and C * programming language features of the CONNECTION machine are also summarized. Various alternate data structures and associated algorithms for nonlinear finite element analysis are discussed and compared. Results are presented which demonstrate that the CONNECTION machine is capable of outperforming the CRAY X-MP/14 by a factor of about 10.

A fluid-structure finite element method for the analysis of reactor safety problems

Abstract A method is presented for the safety analysis of reactor containment structures by means of finite elements. The finite element equations of both fluid and structural elements for arbitrarily large, non-linear response are developed and the way in which they are combined is indicated. Both explicit and implicit integration of the equations in time is considered. Three examples of the application of these methods to the analyses of reactor safety problems are described.

Theory and application of a finite element method for arbitrary Lagrangian-Eulerian fluids and structures

Abstract A coupled model for the analysis of three-dimensional structures interacting with a three-dimensional axisymmetric fluid has been developed. The model is intended for the study of the role of above core structures in core disruptive accidents. Because the fluid model must be capable of interacting with the structure while it experiences large deformations, an Arbitrary Lagrangian-Eulerian (ALE) mesh description, which enables the motion of the nodes to be programmed by the user, was chosen. Both the structural and the fluid model are programmed in a finite element format for the sake of versatility. Example calculations for a two-dimensional bubble problem, which served primarily to verify the computational algorithm for the fluid are presented. For the purpose of examining the capability of the method and simulating the response of above core structures in a CDA, numerous simulations were made of some SRI scale model tests. The results show reasonable agreement with the experiment.

Recent developments in explicit finite element techniques and their application to reactor structures

Abstract A triangular element which requires only one quadrature point per element is described along with its implementation in the nonlinear, explicit time integration program SAFE/RAS. The implementation of an Ilyushin flow law which eliminates the need for integration through the thickness and simple formulas for stable time steps is also described. The performance of the triangular and quadrilateral elements is compared in large deflection, elastic-plastic problems. Applications to the analysis of above-core structures in breeder reactors are also described.

Dynamic response of fast-reactor core subassemblies☆

Abstract A program for predicting the behavior of the hexagonal fuel assembly duct when subjected to internally generated pressures in the LMFBR is described. To a large extent, studies have been made with two-dimensional models of the hexcan. In these problems, the loadings must be restricted to line loads of sufficient length so that axial effects can be neglected. The finite element models range from a single hexcan to models which include both the loaded hexcan, two adjacent rows of hexcans, the coolant layers between hexcans, and the fuel rod assemblies. A nonlinear, transient finite element program called STRAW is used for the analyses. The program accounts for both geometric and material nonlinearities, and has special features for treating the coolant layer between hexcans by a quasi-Eulerian description and vertical flow in the hexcans and layer so that motions of the coolant can be accurately analyzed. The model has been used with loadings ranging from 500 psi to the kilobar range, and has yielded significant results on damage in adjacent assemblies and the restraining effects of the coolant. For example, preliminary results have shown that deformations of the loaded hexcan are reduced by 25 to 50% when the role of the coolant is included and that corner ductility has very large effects on hexcan response.

Post-test analysis for the nonlinear response of an internally pressurized one sixth scale reinforced concrete containment model

Abstract Pretest predictions have been previously made and reported by the Engineering Mechanics Program of the Reactor Analysis and Safety Division for the response of the one sixth scale reinforced concrete model tested by Sandia National Laboratories in July 1987. A series of axisymmetric models were studied with the two-dimensional computer program TEMP-STRESS. This report describes the comparison between the pretest predictions and the experimental results; a post-test analysis with a precracked concrete model is also compared to the pretest predictions and the experimental results. The post-test analysis is in excellent agreement with the experimental results. Explanations are given for the apparent precracked state of the containment vessel.

Concrete cracking simulations for nuclear applications

Abstract The need to understand concrete behavior under high temperatures in the nuclear industry has become rather acute. Previously, concrete has been used in nuclear industry as inexpensive material for construction and also for radiation shielding. Presently, we are concerned with the structural integrity of the containment, subject to accidental exposure of concrete to excessively high temperatures and chemical attack. Consequently, we are now seeking basic understanding of concrete behavior at extreme environmental condition. Indispensible in mathematical modeling of concrete behavior is the constitutive relation. A constitutive model developed by Takahashi [1] has been incorporated into the coupled thermal-stress analysis code, TEMP-STRESS, which gives the stress-strain relation up to the point of cracking. This paper describes the modeling of cracking behavior. Four crack propagation criteria: the J-integral, the energy release rate, the effective strength and the failure surface criterion are examined. Several numerical examples are given. Situations under which one method might be more convenient to use than the others are discussed.