Sierra/SD provides a massively parallel implementation of structural dynamics finite element analysis, required for high fidelity, validated models used in modal, vibration, static and shock analysis of structural systems. This manual describes the theory behind many of the constructs in Sierra/SD. For a more detailed description of how to use Sierra/SD, we refer the reader to User's Manual. Many of the constructs in Sierra/SD are pulled directly from published material. Where possible, these materials are referenced herein. However, certain functions in Sierra/SD are specific to our implementation. We try to be far more complete in those areas. The theory manual was developed from several sources including general notes, a programmer notes manual, the user's notes and of course the material in the open literature.
The “how to” document is designed to help walk the analyst through difficult aspects of software usage. It should supplement both the User’s manual and the Theory document, by providing examples and detailed discussion that reduce learning time for complex set ups. These documents are intended to be used together. We will not formally list all parameters for an input here – see the User’s manual for this. All the examples in the “How To” document are part of the Sierra/SD test suite, and each will run with no modification. The nature of this document casts together a number of rather unrelated procedures. Grouping them is difficult. Please try to use the table of contents and the index as a guide in finding the analyses of interest.
Among the main challenges in shape optimization is the coupling of Finite Element Method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multi-physics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. There are two mathematically equivalent approaches to computing the shape derivative: the volume method, and the boundary method. Each has a major drawback: the boundary method is less accurate, while the volume method is more invasive to the FEM code. Prior implementations of shape derivatives at Sandia have been based on the volume method. We introduce the strip method, which computes shape derivatives on a strip adjacent to the boundary. The strip method makes code coupling simple. Like the boundary method, it queries the state and adjoint solutions at quadrature nodes, but requires no knowledge of the FEM code implementations. At the same time, it exhibits the higher accuracy of the volume method. The development of the strip method also offers us the opportunity to share some lessons learned about implementing the volume method and boundary method, to show shape optimization results on problems of interest, and to begin addressing the other main challenges at hand: constraints on optimized shapes, and their interplay with optimization algorithms.
This document presents tests from the Sierra Structural Mechanics verification test suite. Each of these tests is run nightly with the Sierra/SD code suite and the results of the test checked versus the correct analytic result. For each of the tests presented in this document the test setup, derivation of the analytic solution, and comparison of the Sierra/SD code results to the analytic solution is provided. This document can be used to confirm that a given code capability is verified or referenced as a compilation of example problems.
Sierra/SD provides a massively parallel implementation of structural dynamics finite element analysis, required for high-fidelity, validated models used in modal, vibration, static and shock analysis of weapons systems. This document provides a user's guide to the input for Sierra/SD. Details of input specifications for the different solution types, output options, element types and parameters are included. The appendices contain detailed examples, and instructions for running the software on parallel platforms.
This document presents tests from the Sierra Structural Mechanics verification test suite. Each of these tests is run nightly with the Sierra/SD code suite and the results of the test checked versus the correct analytic result. For each of the tests presented in this document the test setup, derivation of the analytic solution, and comparison of the Sierra/SD code results to the analytic solution is provided. This document can be used to confirm that a given code capability is verified or referenced as a compilation of example problems.
Sierra/SD provides a massively parallel implementation of structural dynamics finite element analysis, required for high fidelity, validated models used in modal, vibration, static and shock analysis of structural systems. This manual describes the theory behind many of the constructs in Sierra/SD. For a more detailed description of how to use Sierra/SD, we refer the reader to Sierra/SD, User's Notes. Many of the constructs in Sierra/SD are pulled directly from published material. Where possible, these materials are referenced herein. However, certain functions in Sierra/SD are specific to our implementation. We try to be far more complete in those areas. The theory manual was developed from several sources including general notes, a programmer notes manual, the user's notes and of course the material in the open literature.
The "how to" document is designed to help walk the analyst through difficult aspects of software usage. It should supplement both the User's manual and the Theory document, by providing examples and detailed discussion that reduce learning time for complex set ups. These documents are intended to be used together. We will not formally list all parameters for an input here — see the User's manual for this. All the examples in the "How To" document are part of the Sierra/SD test suite, and each will run with no modification. The nature of this document casts together a number of rather unrelated procedures. Grouping them is difficult. Please try to use the table of contents and the index as a guide in finding the analyses of interest.
The root mean square (RMS) von Mises stress is a criterion used for assessing the reliability of structures subject to stationary random loading. This work investigates error in RMS von Mises stress and its relationship to the error in acceleration for random vibration analysis. First, a theoretical development of stress-acceleration error is introduced for a simplified problem based on modal stress analysis. Using results from the example as a basis, a similar error relationship is determined for random vibration problems. Finite element analyses of test structures subject to an input acceleration auto-spectral density are performed and results from parametric studies are used to determine error. For a given error in acceleration, a relationship to the error in RMS von Mises stress is established. The resulting relation is used to calculate a bound on the RMS von Mises stress based on the computed accelerations. This error bound is useful in vibration analysis, especially where uncertainty and variability must be thoroughly considered.
Most experimental setups and environment specifications define acceleration loads on the component. However, Sierra Structural Dynamics cannot apply acceleration boundary conditions in modal transient analysis. Modal analysis of these systems and environments must be done through the application of a huge artificial force to a large fictitious point mass. Introducing a large mass into the analysis is a common source of numerical error. In this report we detail a mathematical procedure to directly apply acceleration boundary conditions in modal analyses without the requirement of adding a non-physical mass to the system. We prototype and demonstrate this procedure in Matlab and scope the work required to integrate this procedure into Sierra Structural Dynamics.
There are several methodologies for modeling fasteners in finite element analyses. This work examines the effect of four predominant fastener modeling methods regarding the fatigue of mock hardware that requires fasteners. Typical fastener modeling methods explored in this work consist of a spring method with no preload, a beam method with no preload, a beam method with a preload, and a solid model representation of the fastener with preload. It is found that the different fastener modeling methods produce slightly different fatigue damage predictions, and that this uncertainty in modeling is insignificant as compared to uncertainty in input. Consequently, any of these methods are considered appropriate. In order to make this assertion, multiaxial fatigue methods are investigated and a proportional method is used because of a biaxiality metric.