Constructing accurate statistical models of critical system responses typically requires an enormous amount of data from physical experiments or numerical simulations. Unfortunately, data generation is often expensive and time consuming. To streamline the data generation process, optimal experimental design determines the 'best' allocation of experiments with respect to a criterion that measures the ability to estimate some important aspect of an assumed statistical model. While optimal design has a vast literature, few researchers have developed design paradigms targeting tail statistics, such as quantiles. In this project, we tailored and extended traditional design paradigms to target distribution tails. Our approach included (i) the development of new optimality criteria to shape the distribution of prediction variances, (ii) the development of novel risk-adapted surrogate models that provably overestimate certain statistics including the probability of exceeding a threshold, and (iii) the asymptotic analysis of regression approaches that target tail statistics such as superquantile regression. To accompany our theoretical contributions, we released implementations of our methods for surrogate modeling and design of experiments in two complementary open source software packages, the ROL/OED Toolkit and PyApprox.
Natural and anthropogenic infrasound may travel vast distances, making it an invaluable resource for monitoring phenomena such as nuclear explosions, volcanic eruptions, severe storms, and many others. Typically, these waves are captured using pressure sensors, which cannot encode the direction of arrival—critical information when the source location is not known beforehand. Obtaining this information therefore requires arrays of sensors with apertures ranging from tens of meters to kilometers depending on the wavelengths of interest. This is often impractical in locations that lack the necessary real estate (urban areas, rugged regions, or remote islands); in any case, it requires multiple power, digitizer, and telemetry deployments. Here, the theoretical basis behind a compact infrasound direction of arrival sensor based on the acoustic metamaterials is presented. This sensor occupies a footprint that is orders of magnitude smaller than the span of a typical infrasound array. The diminutive size of the unit greatly expands the locations where it can be deployed. The sensor design is described, its ability to determine the direction of arrival is evaluated, and further avenues of study are suggested.
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.
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.
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 is an engineering structural dynamics code that provides Sandia and other customers a tool to model structural and acoustic physics on large complex physical systems using massively parallel processing. This report provides a detailed overview on Sierra/SD’s most recent physics package: coupled electro-mechanical physics. This capability uses the finite element method to model coupled electro-mechanical physics exhibited by piezoelectric materials. This report provides an applications overview, theory overview, and verification examples demonstrating the electro-mechanical physics modeling capabilities of Sierra/SD.
The “how to” document guides the user through complicated 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.
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].
This paper presents a topology optimization formulation for frequency-domain dynamics to reduce solution dependence upon initial guess and considered loading conditions. Due to resonance phenomena in undamped steady-state dynamics, objectives measuring dynamic response possess many local minima that may represent poor solutions to a design problem, an issue exacerbated for design with respect to multiple frequencies. We propose an extension of the modified error-in-constitutive-equations (MECE) method, used previously in material identification inverse problems, as a new approach for frequency-domain dynamics topology optimization to mitigate these issues. The main idea of the proposed framework is to incorporate an additional penalty-like term in the objective function that measures the discrepancy in the constitutive relations between stresses and strains and between inertial forces and displacements. Then, the design problem is cast within a PDE-constrained optimization formulation in which we seek displacements, stresses, inertial forces, and a density-field solution that minimize our new objective subject to conservation of linear momentum plus some additional constraints. We show that this approach yields superior designs to conventional gradient-based optimization approaches that solely use a functional of displacements as the objective, while strictly enforcing the constitutive equations. The MECE strategy integrates into a density-based topology optimization scheme for void–solid or two-phase material structural design. We highlight the merits of our approach in a variety of scenarios for direct frequency response design, considering multiple frequency load cases and structural objectives.
We develop a generalized stress inversion technique (or the generalized inversion method) capable of recovering stresses in linear elastic bodies subjected to arbitrary cuts. Specifically, given a set of displacement measurements found experimentally from digital image correlation (DIC), we formulate a stress estimation inverse problem as a partial differential equation-constrained optimization problem. We use gradient-based optimization methods, and we accordingly derive the necessary gradient and Hessian information in a matrix-free form to allow for parallel, large-scale operations. By using a combination of finite elements, DIC, and a matrix-free optimization framework, the generalized inversion method can be used on any arbitrary geometry, provided that the DIC camera can view a sufficient part of the surface. We present numerical simulations and experiments, and we demonstrate that the generalized inversion method can be applied to estimate residual stress.
While elastic metasurfaces offer a remarkable and very effective approach to the subwavelength control of stress waves, their use in practical applications is severely hindered by intrinsically narrow band performance. In applications to electromagnetic and photonic metamaterials, some success in extending the operating dynamic range was obtained by using nonlocality. However, while electronic properties in natural materials can show significant nonlocal effects, even at the macroscales, in mechanics, nonlocality is a higher-order effect that becomes appreciable only at the microscales. This study introduces the concept of intentional nonlocality as a fundamental mechanism to design passive elastic metasurfaces capable of an exceptionally broadband operating range. The nonlocal behavior is achieved by exploiting nonlocal forces, conceptually akin to long-range interactions in nonlocal material microstructures, between subsets of resonant unit cells forming the metasurface. These long-range forces are obtained via carefully crafted flexible elements, whose specific geometry and local dynamics are designed to create remarkably complex transfer functions between multiple units. The resulting nonlocal coupling forces enable achieving phase-gradient profiles that are functions of the wavenumber of the incident wave. The identification of relevant design parameters and the assessment of their impact on performance are explored via a combination of semianalytical and numerical models. The nonlocal metasurface concept is tested, both numerically and experimentally, by embedding a total-internal-reflection design in a thin-plate waveguide. Results confirm the feasibility of the intentionally nonlocal design concept and its ability to achieve a fully passive and broadband wave control.
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.
While lattice metamaterials can achieve exceptional energy absorption by tailoring periodically distributed heterogeneous unit cells, relatively little focus has been placed on engineering heterogeneity above the unit-cell level. In this work, the energy-absorption performance of lattice metamaterials with a heterogeneous spatial layout of different unit cell architectures was studied. Such multi-morphology lattices can harness the distinct mechanical properties of different unit cells while being composed out of a single base material. A rational design approach was developed to explore the design space of these lattices, inspiring a non-intuitive design which was evaluated alongside designs based on mixture rules. Fabrication was carried out using two different base materials: 316L stainless steel and Vero White photopolymer. Results show that multi-morphology lattices can be used to achieve higher specific energy absorption than homogeneous lattice metamaterials. Additionally, it is shown that a rational design approach can inspire multi-morphology lattices which exceed rule-of-mixtures expectations.
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 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.
Residual stress is a common result of manufacturing processes, but it is one that is often overlooked in design and qualification activities. There are many reasons for this oversight, such as lack of observable indicators and difficulty in measurement. Traditional relaxation-based measurement methods use some type of material removal to cause surface displacements, which can then be used to solve for the residual stresses relieved by the removal. While widely used, these methods may offer only individual stress components or may be limited by part or cut geometry requirements. Diffraction-based methods, such as X-ray or neutron, offer non-destructive results but require access to a radiation source. With the goal of producing a more flexible solution, this LDRD developed a generalized residual stress inversion technique that can recover residual stresses released by all traction components on a cut surface, with much greater freedom in part geometry and cut location. The developed method has been successfully demonstrated on both synthetic and experimental data. The project also investigated dislocation density quantification using nonlinear ultrasound, residual stress measurement using Electronic Speckle Pattern Interferometry Hole Drilling, and validation of residual stress predictions in Additive Manufacturing process models.
The concept of total-internal-reflection elastic metasurface (TIR-MS)was recently proposed [1]and employed within flexible planar waveguides in order to create highly subwavelength sound-hard barriers impenetrable to low frequency elastic waves. The underlying physical mechanism relies on the design of engineered interfaces exhibiting extreme phase gradients such that any incoming wave at, approximately, any incidence will experience total-internal-reflection conditions. At the design frequency, the metasurface exhibits a large phase gradient such that, in accordance with the generalized Snell's law, the first critical angle is virtually always exceeded. It is worth noting that in practical realizations, the actual total reflection performance might vary depending on the angle of incidence. This dependence is due to the discrete implementation of the metasurface which results in diffraction effects. This paper presents the results of an experimental study that explores the vibration isolation performance of TIR-MS when applied to structures made of complex combinations of different elastic waveguides (e.g. bolted assemblies of beams, plates, and shells). Such system can be seen as a prototypical structure emulating mechanical assemblies of practical interest for many engineering applications. Experimental results confirm that, when the TIR-MS is embedded in the host waveguide, significant vibration isolation capabilities are achieved under quasi-omnidirectional incidence and highly subwavelength excitation conditions (i.e. the ratio of the operating wavelength to the width of the TIR-MS is approximately 5.25). These experimental results suggest new interesting directions to achieve vibration isolation and mechanical energy filtering for practical engineering systems.
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.
Differences in impedance are usually observed when components are tested in fixtures at lower levels of assembly from those in which they are fielded. In this work, the Kansas City National Security Campus (KCNSC) test bed hardware geometry is used to explore the sensitivity of the form of the objective function on the adequate reproduction of relevant response characteristics at the next level of assembly. Inverse methods within Sandia National Laboratories’ Sierra/SD code suite along with the Rapid Optimization Library (ROL) are used for identifying an unknown material (variable shear and bulk modulus) distributed across a predefined fixture volume. Comparisons of the results between time-domain based objective functions are presented. The development of the objective functions, solution sensitivity, and solution convergence will be discussed in the context of the practical considerations required for creating a realizable set of test hardware based on the variable-modulus optimized solutions.
In computational structural dynamics problems, the ability to calibrate numerical models to physical test data often depends on determining the correct constraints within a structure with mechanical interfaces. These interfaces are defined as the locations within a built-up assembly where two or more disjointed structures are connected. In reality, the normal and tangential forces arising from friction and contact, respectively, are the only means of transferring loads between structures. In linear structural dynamics, a typical modeling approach is to linearize the interface using springs and dampers to connect the disjoint structures, then tune the coefficients to obtain sufficient accuracy between numerically predicted and experimentally measured results. This work explores the use of a numerical inverse method to predict the area of the contact patch located within a bolted interface by defining multi-point constraints. The presented model updating procedure assigns contact definitions (fully stuck, slipping, or no contact) in a finite element model of a jointed structure as a function of contact pressure computed from a nonlinear static analysis. The contact definitions are adjusted until the computed modes agree with experimental test data. The methodology is demonstrated on a C-shape beam system with two bolted interfaces, and the calibrated model predicts modal frequencies with <3% total error summed across the first six elastic modes.
This letter presents the concept of the Total Internal Reflection metasurface (TIR-MS) which supports the realization of structure-embedded subwavelength acoustic shields for elastic waves propagating in thin waveguides. The proposed metasurface design exploits extreme phase gradients, implemented via locally resonant elements, in order to achieve operating conditions that are largely beyond the critical angle. Such artificial discontinuity is capable of producing complete reflection of the incoming waves regardless of the specific angle of incidence. From a practical perspective, the TIR-MS behaves as a sound hard barrier that is impenetrable to long-wavelength modes at a selected frequency. The TIR metasurface concept is first conceived for a flat interface embedded in a rectangular waveguide and designed to block longitudinal S0-type guided modes. Then, it is extended to circular plates in order to show how enclosed areas can be effectively shielded by incoming waves. Given the same underlying physics, an equivalent dynamic behavior was also numerically and experimentally illustrated for flexural A0-type guided modes. This study shows numerical and experimental evidence that, when the metasurface is excited at the target frequency, significant vibration isolation can be achieved in the presence of waves having any arbitrary angle of incidence. These results open interesting paths to achieve vibration isolation and energy filtering in certain prototypical structures of interest for practical engineering applications.