Gordon S. Bjorkman

Mesh Convergence Studies for Thin Shell Elements Developed by the ASME Task Group on Computational Modeling

The ASME Task Group on Computational Modeling for Explicit Dynamics was founded in August 2008 for the purpose of creating a quantitative guidance document for the development of finite element models used to analyze energy-limited events using explicit dynamics software. This document will be referenced in the ASME Code Section III, Division 3 and the next revision of NRC Regulatory Guide 7.6 as a means by which the quality of a finite element model may be judged. One portion of the document will be devoted to a series of element convergence studies that can aid designers in establishing the mesh refinement requirements necessary to achieve accurate results for a variety of different elements types in regions of high plastic strain. These convergence studies will also aid reviewers in evaluating the quality of a finite element model and the apparent accuracy of its results. In this paper the authors present the results of a convergence study for an impulsively loaded propped cantilever beam constructed of LS-DYNA thin shell elements using both reduced and full integration. Three loading levels are considered; the first maintains strains within the elastic range, the second induces moderate plastic strains, and the third produces large deformations and large plastic strains.Copyright

The Effect of Gaps on the Impact Response of a Cask Closure Lid

During an impact event, gaps between the various components of a spent fuel transportation cask may create secondary impacts that result in higher dynamic loads than would have occurred if the gaps had not been present. A condition of particular interest is the gap that may exist between the cask internal contents (fuel assemblies) and cask closure lid, and the effect this gap may have on amplifying the response of the closure lid during an impact. Through the use of a simple dynamic model this paper investigates the effect of a secondary impact due to a gap between the cask internals and the cask closure lid on the response of the closure lid during a 30 foot end drop. The dynamic model consists of five components: (1) The equivalent mass of the internal contents, (2) the gap between the contents and cask lid, (3) the stiffness of the cask lid, assumed to be a simply supported circular plate, (4) the equivalent mass of the lid and finally, (5) an impact limiter that applies a constant deceleration force to the cask overpack during impact. In addition, the dynamic model assumes elastic behavior. This is consistent with the Standard Review Plan (NUREG-1617), which recommends that the closure lid bolts and closure lid system within the region of the lid bolts remain elastic in order to demonstrate leak-tightness by finite element analysis. The response results are presented in terms of the Dynamic Load Factor (DLF) for the closure lid. Response is shown to be a nonlinear function of the impact limiter deceleration, gap size and closure lid diameter, thickness and inertial properties. These results provide valuable insights into the parameters that affect response and show the conditions under which gaps of sufficient size may significantly influence response.

Finite Element Mesh Considerations for Reduced Integration Elements

Finite element models of spent fuel casks and canisters that are typically used in impact and impulse analyses may contain tens of thousands of nonlinear elements. These models use explicit time integration methods with small time steps. To achieve reasonable run times, fully integrated elements are replaced with under-integrated elements that use reduced integration procedures. When fully integrated these elements produce a linear strain distribution. Reduced integration, however, results in a constant strain distribution, which requires more elements through the thickness of the canister shell to achieve the same accuracy as fully integrated elements. This paper studies the effect of the number of reduced integration elements through the thickness of the canister shell and the ratio of element height to shell thickness on the accuracy of the strains in regions of high through-thickness bending, such as the junction between the shell and base plate. It is concluded that mesh refinement has a significant effect on the maximum plastic strain response in such regions and that a converged solution may not be attainable within practical limits of mesh refinement, if the results are based solely on the maximum plastic strain on a cross section at a structural discontinuity. The objective is not to chase the stress concentration with ever finer meshes, but rather the objective is to establish a mesh density within the discontinuity region that results in the stresses and strains that are associated with the bending moment that restores compatibility at the structural discontinuity. In this case a converged solution is obtained by investigating the response of other elements on the same cross section that are not located on the surface of the stress concentration at the structural discontinuity. Based on the results, a “rule of thumb” is proposed for mesh refinement in a region of severe structural discontinuity wherein reasonably proportioned reduced integration solid elements are used and plastic strains are evaluated.

Mesh Convergence Studies for Thick Shell Elements Developed by the ASME Special Working Group on Computational Modeling

The ASME Special Working Group on Computational Modeling for Explicit Dynamics was founded in August 2008 for the purpose of creating a quantitative guidance document for the development of finite element models used to analyze energy-limited events using explicit dynamics software. This document will be referenced in the ASME Code Section III, Division 3 and the next revision of NRC Regulatory Guide 7.6 as a means by which the quality of a finite element model may be judged. One portion of the document will be devoted to a series of element convergence studies that can aid designers in establishing the mesh refinement requirements necessary to achieve accurate results for a variety of different element types in regions of high plastic strain. These convergence studies will also aid reviewers in evaluating the quality of a finite element model and the apparent accuracy of its results.In this paper, the authors present the results of a convergence study for an impulsively loaded propped cantilever beam constructed of LS-DYNA thick shell elements using both reduced and selectively reduced integration. A large load is applied to produce large deformations and large plastic strains in the beam. The deformation and plastic strain results are then compared to similar results obtained using thin shell elements and hexahedral elements for the beam mesh.Copyright

Mesh Convergence Studies for Hexahedral Elements Developed by the ASME Special Working Group on Computational Modeling

The ASME Special Working Group on Computational Modeling for Explicit Dynamics was founded in August 2008 for the purpose of creating a quantitative guidance document for the development of finite element models used to analyze energy-limited events using explicit dynamics software. This document will be referenced in the ASME Code Section III, Division 3 and the next revision of NRC Regulatory Guide 7.6 as a means by which the quality of a finite element model may be judged. One portion of the document will be devoted to a series of element convergence studies that can aid designers in establishing the mesh refinement requirements necessary to achieve accurate results for a variety of different element types in regions of high plastic strain. These convergence studies will also aid reviewers in evaluating the quality of a finite element model and the apparent accuracy of its results.In this paper, the authors present the results of a convergence study for an impulsively loaded propped cantilever beam constructed of LS-DYNA hexahedral elements using both reduced and selectively reduced integration. Three loading levels are considered; the first maintains strains within the elastic range, the second induces moderate plastic strains, and the third produces large deformations and large plastic strains.Copyright

Hourglass Control Convergence Studies for Hexahedral Elements Developed by the ASME Special Working Group on Computational Modeling

The ASME Special Working Group on Computational Modeling for Explicit Dynamics was founded in August 2008 for the purpose of creating a quantitative guidance document for the development of finite element models used to analyze energy-limited events using explicit dynamics software. This document will be referenced in the ASME Code Section III, Division 3 and the next revision of NRC Regulatory Guide 7.6 as a means by which the quality of a finite element model may be judged. One portion of the document will be devoted to a series of convergence studies that demonstrates the effect of hourglass control settings on solution convergence for reduced integration elements. These convergence studies will demonstrate the importance of selecting an appropriate hourglass control setting to achieve accurate results for large deformation simulations using reduced integration elements.In this paper, the authors present the results of a convergence study for an impulsively loaded propped cantilever beam constructed of LS-DYNA reduced integration hexahedral elements using different hourglass control settings. A large load is applied to produce large deformations and large plastic strains in the beam.Copyright

When is a crush test not a crush test? or What constitutes a valid crush test?

Abstract Recent discussions at the international level are elaborated regarding the intent and method for clarifying acceptable package/drop mass orientations for the dynamic crush test that is required for some Type B and some Type A fissile radioactive material packages. Coverage includes part of the discussions that occurred at an International Atomic Energy Agency Consultants Services Meeting convened to discuss this issue in September 2008.

The Buckling of Fuel Rods Under Inertia Loading

The buckling analysis of fuel rods during an end drop impact of a spent fuel transportation cask has traditionally been performed to demonstrate the structural integrity of the fuel rod cladding or the integrity of the fuel geometry in criticality evaluations for a cask drop event. The actual calculation of the fuel rod buckling load, however, has been the subject of some controversy, with estimates of the critical buckling load differing by as much as a factor of 5. Typically, in the buckling analysis of a fuel rod, assumptions are made regarding the percentage of fuel mass that is bonded to or that participates with the cladding during the buckling process, with estimates ranging from 0 to 100%. The greater the percentage of fuel mass that is assumed to be bonded to the cladding the higher the inertia loads on the cladding, and, therefore, the lower the “g” value at which buckling occurs. However, these solutions do not consider displacement compatibility between the fuel and the cladding during the buckling process. By invoking displacement compatibility between the fuel column and the cladding column, this paper presents an exact solution for the buckling of fuel rods under inertia loading. The results show that the critical inertia load magnitude for the buckling of a fuel rod depends on the weight of the cladding and the total weight of the fuel, regardless of the percentage of fuel mass that is assumed to be attached to or participate with the cladding in the buckling process. Therefore, 100% of the fuel always participates in the buckling of a fuel rod under inertia loading.

Strain-Based Acceptance Criteria for Inelastic Analysis

Modern finite element codes used in the design of nuclear material transportation and storage casks can readily calculate the response of the packages beyond the elastic regime. These packages are designed to protect workers, the public, and the environment from the harmful effects of the transported radioactive material following a sequence of hypothetical accident conditions. Hypothetical accidents considered for transport packages include a 9-meter free drop onto an essentially unyielding target and a 1-meter free fall onto a 30-cm diameter puncture spike. For storage casks, accident conditions can include drops, tip-over, and aircraft impact. All of these accident events are energy-limited rather than load-limited, as is typically the case for boilers and pressure vessels. Therefore, it makes sense to have analysis acceptance criteria that are more closely related to absorbed energy than to applied load. Strain-based acceptance criteria are the best way to meet this objective. As cask vendors’ ability to perform non-linear impact analysis has improved, the need for a code-based method to interpret the results of this type of analysis has increased. The ASME Section III Working Group on Design of Division 3 Containments is working with Section III Working Group Design Methodology to develop strain-based acceptance criteria to use within the ASME Code for energy-limited events. This paper will briefly discuss the efforts within the ASME, detail the advantages of using strain-based criteria, discuss the problem areas associated with establishing strain-based criteria, and provide insights into inelastic analyses as applied to radioactive material transportation and storage casks in general. The views expressed represent those of the authors and not necessarily those of their respective organizations or the ASME.Copyright