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NASA NTRS1987

A probabilistic Hu-Washizu variational principle

A Probabilistic Hu-Washizu Variational Principle (PHWVP) for the Probabilistic Finite Element Method (PFEM) is presented. This formulation is developed for both linear and nonlinear elasticity. The PHWVP allows incorporation of the probabilistic distributions for the constitutive law, compatibility condition, equilibrium, domain and boundary conditions into the PFEM. Thus, a complete probabilistic analysis can be performed where all aspects of the problem are treated as random variables and/or fields. The Hu-Washizu variational formulation is available in many conventional finite element codes thereby enabling the straightforward inclusion of the probabilistic features into present codes.

Liu, W. K.↗

NASA NTRS1985

Spartan service module finite element modeling technique and analysis

Sounding rockets have served as a relatively inexpensive and easy method of carrying experiments into the upper atmosphere. Limited observation time and pointing capabilities suggested the development of a new sounding rocket type carrier compatible with NASA's Space Transportation System. This concept evolved into the Spartan program, now credited with a successful Spartan 101 mission launched in June 1985. The next series of Spartans will use a service module primary structure. This newly designed reusable and universal component in the Spartan carrier system required thorough analysis and evaluation for flight certification. Using advanced finite element modeling techniques, the structure was analyzed and determined acceptable by meeting strict design goals and will be tested for verification of the analytical results.

Lindenmoyer, A. J.↗

NASA NTRS1978

Recent advances in thermostructural finite element analysis

A comparison study is described which has indicated that the finite element and lumped parameter methods are comparable for steady-state conduction/convection analyses. The finite element model was advantageous because of the ease of model verification with computer graphics. Some problems encountered in constructing compatible thermal and structural models have indicated the need for further methodology developments to automate the transition between thermal and structural analyses. The need for more efficient finite element nonlinear transient algorithms has been cited. With further development in the thermal analysis area, the finite element method offers high potential for an integrated thermal/structural analysis capability.

Thornton, E. A.↗

DOE OSTI2022

Subcell limiting strategies for discontinuous Galerkin spectral element methods

Here, we present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct compatible low order finite volume (FV) type discretizations that allow for convex blending with the high-order variant with the goal of guaranteeing additional properties, such as bounds on physical quantities and/or guaranteed entropy dissipation. For an implementation of this main strategy, four main ingredients are identified that may be combined in a flexible manner: (i) a nodal high-order DG method on Legendre–Gauss–Lobatto nodes, (ii) a compatible robust subcell FV scheme, (iii) a convex combination strategy for the two schemes, which can be element-wise or subcell-wise, and (iv) a strategy to compute the convex blending factors, which can be either based on heuristic troubled-cell indicators, or using ideas from flux-corrected transport methods. By carefully designing the metric terms of the subcell FV method, the resulting methods can be used on unstructured curvilinear meshes, are locally conservative, can handle strong shocks efficiently while directly guaranteeing physical bounds on quantities such as density, pressure or entropy. We further show that it is possible to choose the four ingredients to recover existing methods such as a provably entropy dissipative subcell shock-capturing approach or a sparse invariant domain preserving approach. We test the versatility of the presented strategies and mix and match the four ingredients to solve challenging simulation setups, such as the KPP problem (a hyperbolic conservation law with non-convex flux function), turbulent and hypersonic Euler simulations, and MHD problems featuring shocks and turbulence.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2001

Multifunctional Collaborative Modeling and Analysis Methods in Engineering Science

Engineers are challenged to produce better designs in less time and for less cost. Hence, to investigate novel and revolutionary design concepts, accurate, high-fidelity results must be assimilated rapidly into the design, analysis, and simulation process. This assimilation should consider diverse mathematical modeling and multi-discipline interactions necessitated by concepts exploiting advanced materials and structures. Integrated high-fidelity methods with diverse engineering applications provide the enabling technologies to assimilate these high-fidelity, multi-disciplinary results rapidly at an early stage in the design. These integrated methods must be multifunctional, collaborative, and applicable to the general field of engineering science and mechanics. Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple-method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized. The multifunctional methodology presented provides an effective mechanism by which domains with diverse idealizations are interfaced. This capability rapidly provides the high-fidelity results needed in the early design phase. Moreover, the capability is applicable to the general field of engineering science and mechanics. Hence, it provides a collaborative capability that accounts for interactions among engineering analysis methods.

Ransom, Jonathan B.↗

NASA NTRS2001

On Multifunctional Collaborative Methods in Engineering Science

Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized.

Ransom, Jonathan B.↗

NASA NTRS2004

Integrated Force Method Solution to Indeterminate Structural Mechanics Problems

Strength of materials problems have been classified into determinate and indeterminate problems. Determinate analysis primarily based on the equilibrium concept is well understood. Solutions of indeterminate problems required additional compatibility conditions, and its comprehension was not exclusive. A solution to indeterminate problem is generated by manipulating the equilibrium concept, either by rewriting in the displacement variables or through the cutting and closing gap technique of the redundant force method. Compatibility improvisation has made analysis cumbersome. The authors have researched and understood the compatibility theory. Solutions can be generated with equal emphasis on the equilibrium and compatibility concepts. This technique is called the Integrated Force Method (IFM). Forces are the primary unknowns of IFM. Displacements are back-calculated from forces. IFM equations are manipulated to obtain the Dual Integrated Force Method (IFMD). Displacement is the primary variable of IFMD and force is back-calculated. The subject is introduced through response variables: force, deformation, displacement; and underlying concepts: equilibrium equation, force deformation relation, deformation displacement relation, and compatibility condition. Mechanical load, temperature variation, and support settling are equally emphasized. The basic theory is discussed. A set of examples illustrate the new concepts. IFM and IFMD based finite element methods are introduced for simple problems.

Patnaik, Surya N.↗

NASA NTRS2002

Fidelity of the Integrated Force Method Solution

The theory of strain compatibility of the solid mechanics discipline was incomplete since St. Venant's 'strain formulation' in 1876. We have addressed the compatibility condition both in the continuum and the discrete system. This has lead to the formulation of the Integrated Force Method. A dual Integrated Force Method with displacement as the primal variable has also been formulated. A modest finite element code (IFM/Analyzers) based on the IFM theory has been developed. For a set of standard test problems the IFM results were compared with the stiffness method solutions and the MSC/Nastran code. For the problems IFM outperformed the existing methods. Superior IFM performance is attributed to simultaneous compliance of equilibrium equation and compatibility condition. MSC/Nastran organization expressed reluctance to accept the high fidelity IFM solutions. This report discusses the solutions to the examples. No inaccuracy was detected in the IFM solutions. A stiffness method code with a small programming effort can be improved to reap the many IFM benefits when implemented with the IFMD elements. Dr. Halford conducted a peer-review on the Integrated Force Method. Reviewers' response is included.

Hopkins, Dale↗

NASA NTRS1992

Improved accuracy for finite element structural analysis via a new integrated force method

A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools.

Patnaik, Surya N.↗

NASA NTRS1992

Improved accuracy for finite element structural analysis via an integrated force method

Patnaik, S. N.↗

NASA NTRS1991

A Lagrange multiplier based divide and conquer finite element algorithm

A novel domain decomposition method based on a hybrid variational principle is presented. Prior to any computation, a given finite element mesh is torn into a set of totally disconnected submeshes. First, an incomplete solution is computed in each subdomain. Next, the compatibility of the displacement field at the interface nodes is enforced via discrete, polynomial and/or piecewise polynomial Lagrange multipliers. In the static case, each floating subdomain induces a local singularity that is resolved very efficiently. The interface problem associated with this domain decomposition method is, in general, indefinite and of variable size. A dedicated conjugate projected gradient algorithm is developed for solving the latter problem when it is not feasible to explicitly assemble the interface operator. When implemented on local memory multiprocessors, the proposed methodology requires less interprocessor communication than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory and compares favorably with factorization based parallel direct methods.

Farhat, C.↗

NASA NTRS1993

A global/local analysis method for treating details in structural design

A method for analyzing global/local behavior of plate and shell structures is described. In this approach, a detailed finite element model of the local region is incorporated within a coarser global finite element model. The local model need not be nodally compatible (i.e., need not have a one-to-one nodal correspondence) with the global model at their common boundary; therefore, the two models may be constructed independently. The nodal incompatibility of the models is accounted for by introducing appropriate constraint conditions into the potential energy in a hybrid variational formulation. The primary advantage of this method is that the need for transition modeling between global and local models is eliminated. Eliminating transition modeling has two benefits. First, modeling efforts are reduced since tedious and complex transitioning need not be performed. Second, errors due to the mesh distortion, often unavoidable in mesh transitioning, are minimized by avoiding distorted elements beyond what is needed to represent the geometry of the component. The method is applied reduced to a plate loaded in tension and transverse bending. The plate has a central hole, and various hole sixes and shapes are studied. The method is also applied to a composite laminated fuselage panel with a crack emanating from a window in the panel. While this method is applied herein to global/local problems, it is also applicable to the coupled analysis of independently modeled components as well as adaptive refinement.

Aminpour, Mohammad A.↗

NASA NTRS2008

Integrated Force Method for Indeterminate Structures

Two methods of solving indeterminate structural-mechanics problems have been developed as products of research on the theory of strain compatibility. In these methods, stresses are considered to be the primary unknowns (in contrast to strains and displacements being considered as the primary unknowns in some prior methods). One of these methods, denoted the integrated force method (IFM), makes it possible to compute stresses, strains, and displacements with high fidelity by use of modest finite-element models that entail relatively small amounts of computation. The other method, denoted the completed Beltrami Mitchell formulation (CBMF), enables direct determination of stresses in an elastic continuum with general boundary conditions, without the need to first calculate displacements as in traditional methods. The equilibrium equation, the compatibility condition, and the material law are the three fundamental concepts of the theory of structures. For almost 150 years, it has been commonly supposed that the theory is complete. However, until now, the understanding of the compatibility condition remained incomplete, and the compatibility condition was confused with the continuity condition. Furthermore, the compatibility condition as applied to structures in its previous incomplete form was inconsistent with the strain formulation in elasticity.

Hopkins, Dale A.↗

DOE OSTI2021

Modeling and analyzing parasitic parameters in high frequency converters

This research focuses on electromagnetic interference (EMI) / electromagnetic compatibility (EMC) design and analysis in power electronics systems. To limit the EMI under the standards, different methods and strategies are investigated. Parasitic parameters of high frequency (HF) transformer are analyzed using a novel analytical method, finite element method (FEM), and experimental measurements for different structures and windings arrangements. Also, the magnetic field, electric field, electric displacement, and electric potential distribution are simulated and analyzed. Moreover, a high voltage system is considered and analyzed to improve the EMC. The EMI propagation paths are analyzed. The EMI noise level of the system is obtained and compared to the IEC61800-3 standard. To improve the EMC, the parasitic parameters of the transformer, as the main path of EMI circulation, are analyzed and optimized to block the propagation. Furthermore, the geometry structure of the HF transformer is optimized to lower the parasitics in the system. Three pareto-optimal techniques are investigated for the optimization. The models and results are verified by 3D-FEM and experimental results for several given scenarios. Furthermore, the EMC modeling and conducted EMI analysis are developed for a system including an AC-DC-DC power supply (rectifier and dual active bridge (DAB) converter). Moreover, the common mode (CM) EMI noise propagation through the system is discussed and the noise sources and effect of components on the noise are analyzed. Additionally, the CM impedance of different parts of the system and the noise levels are discussed. Finally, EMI attenuation techniques were applied to the system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Non-destructive simulation of node defects in additively manufactured lattice structures

Additive Manufacturing (AM), commonly referred to as 3D printing, offers the ability to not only fabricate geometrically complex lattice structures but parts in which lattice topologies in-fill volumes bounded by complex surface geometries. However, current AM processes produce defects on the strut and node elements which make up the lattice structure. This creates an inherent difference between the as-designed and as-fabricated geometries, which negatively affects predictions (via numerical simulation) of the lattice’s mechanical performance. Although experimental and numerical analysis of an AM lattice’s bulk structure, unit cell and struts have been performed, there exists almost no research data on the mechanical response of the individual as-manufactured lattice node elements. Here we propose a methodology that, for the first time, allows non-destructive quantification of the mechanical response of node elements within an as-manufactured lattice structure. A custom-developed tool is used to extract and classify each individual node geometry from micro-computed tomography scans of an AM fabricated lattice. Voxel-based finite element meshes are generated for numerical simulation and the mechanical response distribution is compared to that of the idealised computer-aided design model. The method demonstrates compatibility with Uncertainty Quantification methods that provide opportunities for efficient prediction of a population of nodal responses from sampled data. Overall, the non-destructive and automated nature of the node extraction and response evaluation is promising for its application in qualification and certification of additively manufactured lattice structures.

36 MATERIALS SCIENCE↗

NASA NTRS1984

Spectral methods for exterior elliptic problems

Spectral approximations for exterior elliptic problems in two dimensions are discussed. As in the conventional finite difference or finite element methods, the accuracy of the numerical solutions is limited by the order of the numerical farfield conditions. A spectral boundary treatment is introduced at infinity which is compatible with the infinite order interior spectral scheme. Computational results are presented to demonstrate the spectral accuracy attainable. Although a simple Laplace problem is examined, the analysis covers more complex and general cases.

Canuto, C.↗

DOE OSTI2020

Initial development and verification of a primary load design method based on elastic-perfectly plastic analysis

This report describes a new primary load design method to supplement the current design-by-elastic-analysis rules in Section III, Division 5, Subsection HB, Subpart B of the ASME Boiler and Pressure Vessel Code, covering the design and construction of Class A high temperature nuclear structural components. The main objectives for the new design method are to provide a procedure that can be applied to components with complicated geometries and to simplify the primary load design process by providing rules more compatible with modern finite element analysis. The report includes a complete set of design rules, presented as a draft ASME Code Case, as well as a commentary on the rules and a set of verification problems. The verification design problems demonstrate the new primary load design rules produce safe, efficient components when compared to the current Division 5 approach, while greatly simplifying the design analysis process.

42 ENGINEERING↗

NASA NTRSDate not supplied

Development of Acoustic Mufflers for Cabin Noise Reduction in Orion Spacecraft

Controlling cabin acoustic noise levels in the Crew Module (CM) of the Orion spacecraft is critical to ensure adequate speech intelligibility, to avoid fatigue, and prevent any possibility of temporary and permanent hearing loss to the crew. The primary source of cabin noise for the on-orbit phase of the mission is from the Environmental Control and Life Support System (ECLSS) which recycles and conditions breathing air and maintains cabin pressurization through its duct network and components. Unfortunately, as a side effect, noise from the ECLSS fans propagates through theses ducts and emanate into the cabin habitable volume via the ECLSS inlet and outlets. To mitigate excessive duct-borne noise, two ECLSS mufflers have been designed to provide significant acoustic transmission loss (TL) so that the cabin noise requirements can be met. Each muffler is meant to be installed in the ducting of the ECLSS air inlet and outlet sides, respectively. Packaging constraints and tight volume requirements necessitated the mufflers to be of complex geometry and compatible with the bends of the ECLSS duct layout. To design and characterize the acoustic performance of the inlet and outlet mufflers, computational acoustic models were developed using the Finite Element Method (FEM) with 𝑤𝑎𝑣𝑒଺ vibroacoustic software. Characterization of the acoustic material and perforations in the mufflers were addressed with poroelastic theory. Once the mufflers were designed on paper and its TL predicted, prototypes of these mufflers were created using additive manufacturing. The muffler prototypes were subsequently tested for acoustic TL in the laboratory with various con-figurations of acoustic materials. Comparing the analytical predictions to the test performance yielded excellent correlation for acoustic TL and demonstrated significant broadband noise attenuation. The ECLSS mufflers are currently scheduled to be installed on the Artemis II Crew Module (CM) of the Orion spacecraft and will provide significant cabin comfort to crew during the mission.

Indranil Dandaroy↗