In this work, we present modal-based methods for model calibration in structural dynamics, and address several key challenges in the solution of gradient-based optimization problems with eigenvalues and eigenvectors, including the solution of singular Helmholtz problems encountered in sensitivity calculations, non-differentiable objective functions caused by mode swapping during optimization, and cases with repeated eigenvalues. Unlike previous literature that relied on direct solution of the eigenvector adjoint equations, we present a parallel iterative domain decomposition strategy (Adjoint Computation via Modal Superposition with Truncation Augmentation) for the solution of the singular Helmholtz problems. For problems with repeated eigenvalues we present a novel Mode Separation via Projection algorithm, and in order to address mode swapping between inverse iterations we present a novel Injective mode ordering metric. We present the implementation of these methods in a massively parallel finite element framework with the ability to use measured modal data to extract unknown structural model parameters from large complex problems. A series of increasingly complex numerical examples are presented that demonstrate the implementation and performance of the methods in a massively parallel finite element framework [7,5], using gradient-based optimization techniques in the Rapid Optimization Library (ROL) [21].
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.
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.
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.
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.
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.
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.
We expand the second-order fluid-structure coupling scheme of Farhat et al. (1998, "Load and Motion Transfer Algorithms for 19 Fluid/Structure Interaction Problems With Non-Matching Discrete Interfaces: Momentum and Energy Conservation, Optimal Discretization and Application to Aeroelasticity,"Comput. Methods Appl. Mech. Eng., 157(1-2), pp. 95-114; 2006, "Provably Second-Order Time-Accurate Loosely-Coupled Solution Algorithms for Transient Nonlinear Computational Aeroelasticity,"Comput. Methods Appl. Mech. Eng., 195(17), pp. 1973-2001) to structural acoustics. The staggered structural acoustics solution method is demonstrated to be second-order accurate in time, and numerical results are compared to a monolithically coupled system. The partitioned coupling method is implemented in the Sierra Mechanics software suite, allowing for the loose coupling of time domain acoustics in sierra/sd to structural dynamics (sierra/sd) or solid mechanics (sierra/sm). The coupling is demonstrated to work for nonconforming meshes. Results are verified for a one-dimensional piston, and the staggered and monolithic results are compared to an exact solution. Huang, H. (1969, "Transient Interaction of Plane Acoustic Waves With a Spherical Elastic Shell,"J. Acoust. Soc. Am., 45(3), pp. 661-670) sphere scattering problem with a spherically spreading acoustic load demonstrates parallel capability on a complex problem. Our numerical results compare well for a bronze plate submerged in water and sinusoidally excited (Fahnline and Shepherd, 2017, "Transient Finite Element/Equivalent Sources Using Direct Coupling and Treating the Acoustic Coupling Matrix as Sparse,"J. Acoust. Soc. Am., 142(2), pp. 1011-1024).
This work explores how High Perforrnance Computing is enabling acoustic solutions across a wide-range ofscience and engineering applications that were historically intractable.
Inverse problems arise in a wide range of applications, whenever unknown model parameters cannot be measured directly. Instead, the unknown parameters are estimated using experimental data and forward simulations. Thermal inverse problems, such as material characterization problems, are often large-scale and transient. Therefore, they require intrusive adjoint-based gradient implementations in order to be solved efficiently. The capability to solve large-scale transient thermal inverse problems using an adjoint-based approach was recently implemented in SNL Sierra Mechanics, a massively parallel capable multiphysics code suite. This report outlines the theory, optimization formulation, and path taken to implement thermal inverse capabilities in Sierra within a unit test framework. The capability utilizes Sierra/Aria and Sierra/Fuego data structures, the Rapid Optimization Library, and an interface to the Sierra/InverseOpt library. The existing Sierra/Aria time integrator is leveraged to implement a time-dependent adjoint solver.
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.
The integrity of engineering structures is often compromised by embedded surfaces that result from incomplete bonding during the manufacturing process, or initiation of damage from fatigue or impact processes. Examples include delaminations in composite materials, incomplete weld bonds when joining two components, and internal crack planes that may form when a structure is damaged. In many cases the areas of the structure in question may not be easily accessible, thus precluding the direct assessment of structural integrity. In this paper, we present a gradient-based, partial differential equation (PDE)-constrained optimization approach for solving the inverse problem of interface detection in the context of steady-state dynamics. An objective function is defined that represents the difference between the model predictions of structural response at a set of spatial locations, and the experimentally measured responses. One of the contributions of our work is a novel representation of the design variables using a density field that takes values in the range [0,1]andraised and raised to an integer exponent that promotes solutions to be near the extrema of the range. The density field is combined with the penalty method for enforcing a zero gap condition and realizing partially bonded surfaces. The use of the penalty method with a density field representation leads to objective functions that are continuously differentiable with respect to the unknown parameters, enabling the use of efficient gradient-based optimization algorithms. Numerical examples of delaminated plates are presented to demonstrate the feasibility of the approach.
Sierra/SD is a structural dynamics finite element software package that is known for its scalability and performance on DOE supercomputers. While there are historical documents demonstrating weak and strong scaling on DOE systems such as Redsky, no such formal studies have been done on modern architectures. This report demonstrates that Sierra/SD still scales on modern architectures. Non structured meshes in the shape of an I-Beam are solved in sizes ranging from fifty thousand degrees of freedom in serial up to one and a half billion degrees of freedom on over eighteen thousand processors using only default solver options. The report serves as a baseline for users to estimate computation cost of finite element analyses in Sierra/SD, understand how solver options relate to computational costs, and pick optimal processor counts to solve a given problem size, as well as a baseline for evaluating computational cost and scalability on next generation architectures.
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.
Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and how this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this paper, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. This provides an additional advantage of PML over the infinite element approach.
