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At least 1,261 records · Page 70

SAPNEW: Parallel finite element code for thin shell structures on the Alliant FX-80

The finite element method has proven to be an invaluable tool for analysis and design of complex, high performance systems, such as bladed-disk assemblies in aircraft turbofan engines. However, as the problem size increase, the computation time required by conventional computers can be prohibitively high. Parallel processing computers provide the means to overcome these computation time limits. This report summarizes the results of a research activity aimed at providing a finite element capability for analyzing turbomachinery bladed-disk assemblies in a vector/parallel processing environment. A special purpose code, named with the acronym SAPNEW, has been developed to perform static and eigen analysis of multi-degree-of-freedom blade models built-up from flat thin shell elements. SAPNEW provides a stand alone capability for static and eigen analysis on the Alliant FX/80, a parallel processing computer. A preprocessor, named with the acronym NTOS, has been developed to accept NASTRAN input decks and convert them to the SAPNEW format to make SAPNEW more readily used by researchers at NASA Lewis Research Center.

Kamat, Manohar P.↗

Tenth NASTRAN User's Colloquium

The development of the NASTRAN computer program, a general purpose finite element computer code for structural analysis, was discussed. The application and development of NASTRAN is presented in the following topics: improvements and enhancements; developments of pre and postprocessors; interactive review system; the use of harmonic expansions in magnetic field problems; improving a dynamic model with test data using Linwood; solution of axisymmetric fluid structure interaction problems; large displacements and stability analysis of nonlinear propeller structures; prediction of bead area contact load at the tire wheel interface; elastic plastic analysis of an overloaded breech ring; finite element solution of torsion and other 2-D Poisson equations; new capability for elastic aircraft airloads; usage of substructuring analysis in the get away special program; solving symmetric structures with nonsymmetric loads; evaluation and reduction of errors induced by Guyan transformation.

Source record↗

Evolutionary Optimization of a Geometrically Refined Truss

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.

Hull, P. V.↗

A transient near to far field transformation method and verification benchmarking procedure

The numerical calculation of electromagnetic far fields in the time-domain requires a near to far field transformation (NTFF) method. While time-domain NTFF methods for popular finite-difference time-domain (FDTD) approaches are well established, there is little discourse on NTFF methods for finite-element time-domain (FETD) codes. Here, this work is concerned with the development of an NTFF method for the Empire FETD code, which utilizes curl and divergence conforming elements. This discretization presents a difficulty in obtaining the equivalent electric current for the NTFF. Straightforward finite element interpolation of the fields is shown to give poor accuracy. Alternative interpolation methods are recommended. An expanding magnetic quadrupole pulse benchmark problem, which is fully developed in the appendices, provides the basis for quantitative comparison.

FETD↗

Modeling and analysis of mixed convection stagnation point flow of nanofluid towards a stretching surface: OHAM and FEM approach

A theoretical study of mixed convection stagnation point flow towards a stretching surface is presented. The governing boundary layer equations are transformed into a set of highly nonlinear ordinary differential equations using suitable similarity transforms. The semi-analytical solution is obtained using optimal homotopy analysis method (OHAM) and the numerical solution is obtained via finite element method (FEM). Solutions obtained via two different approaches are in excellent agreement, which validates the accuracy of present analysis. In a special case, the present OHAM solution is also validated with the earlier available results. Effect of pertinent flow parameters on the skin friction coefficient and Nusselt number is presented in tabular form, whereas the velocity, temperature and nanoparticle distribution are presented in graphical forms. Further, a quadratic multiple regression analysis on numeric data of skin friction coefficient and Nusselt number is performed. The findings suggest that velocity slip assists the fluid motion in presence of buoyancy forces, whereas it exhibits a retarding nature on fluid motion when no buoyancy forces exist.

97 MATHEMATICS AND COMPUTING↗

Joint inversion of electromagnetic measurements for the determination of water saturation profiles in concrete structures

Highlights: • DC-electrical and dielectric data are combined to estimate concrete saturation degree. • A joint inversion approach of the electromagnetic measurements is proposed. • The sensitivity of the measurements to the saturation model parameters is analysed. • The new joint approach was developed and is applied to synthetic and real data. • The benefits of the joint approach over the inversion of one data type are highlighted. Water saturation profiles in concrete are essential to assess its durability and can be determined using non-destructive techniques, especially the electric and the capacitive methods. In this paper, we propose a new inversion scheme where both resistivity and permittivity measurements are inverted jointly to retrieve the saturation profile. The finite element method is used to model the measurements in 3D, the concrete having a saturation profile with depth, represented by a continuous model taking the form of a Weibull curve with four parameters. A non-linear least-squares optimization based on the Levenberg-Marquardt scheme is developed for the inversion of measurements. Results show that information gathered from both measurements enriches the reconstructed profile, leading to a more reliable estimation of saturation profiles. We believe that the joint inversion method herein developed could lead to the study of more complex phenomena, such as the coupled water-chloride ingress.

36 MATERIALS SCIENCE↗

Anisotropic elastoplastic response of double-porosity media

Here we present a continuum framework to simulate fluid flow through anisotropic elastoplastic media with double porosity. Two effective stress measures σ' and δ" emerge from the thermodynamic formulation, which are energy-conjugate to the elastic and plastic components of strain, respectively. Both effective stress measures can be expressed as a combination of the total Cauchy stress σ and the average pore pressure $\bar{p}$ in the two pore scales. In the effective stress for elasticity, $\bar{p}$ is scaled with a rank-2 Biot tensor, whereas the effective stress for plasticity follows the Terzaghi form in which $\bar{p}$ is scaled by the Kronecker delta. The Biot tensor and storage coefficients are derived as functions of elasticity parameters and porosities. A mixed finite element formulation is introduced to discretize the domain and solve initial boundary-value problems. A stabilization scheme is employed on equal-order interpolation for both displacement and pressure fields throughout the entire range of drainage responses. Numerical simulations reproduce the hydromechanical response of Opalinus shale in one-dimensional consolidation tests throughout the range of primary and secondary consolidation under different external loads. Numerical simulations of the consolidation of a rectangular domain subjected to a strip load demonstrate the efficacy of the proposed stabilization scheme, as well as illustrate the impacts of stress history, mass transfer, and different pore systems on the hydromechanical response.

42 ENGINEERING↗

A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction

This study presents a novel application of the hybridizable discontinuous Galerkin (HDG) finite element method to the multi-physics simulation of coupled fluid–structure interaction (FSI) problems. Recent applications of the HDG method have primarily been for single-physics problems including both solids and fluids, which are necessary building blocks for FSI modeling. Utilizing these established models, HDG formulations for linear elastostatics, a nonlinear elastodynamic model, and arbitrary Lagrangian–Eulerian Navier–Stokes are derived. The elasticity formulations are written in a Lagrangian reference frame, with the nonlinear formulation restricted to hyperelastic materials. With these individual solid and fluid formulations, the remaining challenge in FSI modeling is coupling together their disparate mathematics on the fluid–solid interface. This coupling is presented, along with the resultant HDG FSI formulation. Verification of the component models, through the method of manufactured solutions, is performed and each model is shown to converge at the expected rate. The individual components, along with the complete FSI model, are then compared to the benchmark problems proposed by Turek and Hron [1]. The solutions from the HDG formulation presented in this work trend towards the benchmark as the spatial polynomial order and the temporal order of integration are increased.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Safety assessment of historical masonry churches based on pre-assigned kinematic limit analysis, FE limit and pushover analyses

This study presents some results of a comprehensive numerical analysis on three masonry churches damaged by the recent Emilia-Romagna (Italy) seismic events occurred in May 2012. The numerical study comprises: (a) pushover analyses conducted with a commercial code, standard nonlinear material models and two different horizontal load distributions; (b) FE kinematic limit analyses performed using a non-commercial software based on a preliminary homogenization of the masonry materials and a subsequent limit analysis with triangular elements and interfaces; (c) kinematic limit analyses conducted in agreement with the Italian code and based on the a-priori assumption of preassigned failure mechanisms, where the masonry material is considered unable to withstand tensile stresses. All models are capable of giving information on the active failure mechanism and the base shear at failure, which, if properly made non-dimensional with the weight of the structure, gives also an indication of the horizontal peak ground acceleration causing the collapse of the church. The results obtained from all three models indicate that the collapse is usually due to the activation of partial mechanisms (apse, façade, lateral walls, etc.). Moreover the horizontal peak ground acceleration associated to the collapse is largely lower than that required in that seismic zone by the Italian code for ordinary buildings. These outcomes highlight that structural upgrading interventions would be extremely beneficial for the considerable reduction of the seismic vulnerability of such kind of historical structures.

42 ENGINEERING↗

Contact kinematics of biomimetic scales

Dermal scales, prevalent across biological groups, considerably boost survival by providing multifunctional advantages. Here, we investigate the nonlinear mechanical effects of biomimetic scale like attachments on the behavior of an elastic substrate brought about by the contact interaction of scales in pure bending using qualitative experiments, analytical models, and detailed finite element (FE) analysis. Our results reveal the existence of three distinct kinematic phases of operation spanning linear, nonlinear, and rigid behavior driven by kinematic interactions of scales. The response of the modified elastic beam strongly depends on the size and spatial overlap of rigid scales. The nonlinearity is perceptible even in relatively small strain regime and without invoking material level complexities of either the scales or the substrate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Magnetic tweezers with high permeability electromagnets for fast actuation of magnetic beads

As a powerful and versatile scientific instrument, magnetic tweezers have been widely used in biophysical research areas, such as mechanical cell properties and single molecule manipulation. If one wants to steer bead position, the nonlinearity of magnetic properties and the strong position dependence of the magnetic field in most magnetic tweezers lead to quite a challenge in their control. In this article, we report multi-pole electromagnetic tweezers with high permeability cores yielding high force output, good maneuverability, and flexible design. For modeling, we adopted a piece-wise linear dependence of magnetization on field to characterize the magnetic beads. We implemented a bi-linear interpolation of magnetic field in the work space, based on a lookup table obtained from finite element simulation. The electronics and software were custom-made to achieve high performance. In addition, the effects of dimension and defect on structure of magnetic tips also were inspected. In a workspace with size of 0.1 × 0.1 mm{sup 2}, a force of up to 400 pN can be applied on a 2.8 μm superparamagnetic bead in any direction within the plane. Because the magnetic particle is always pulled towards a tip, the pulling forces from the pole tips have to be well balanced in order to achieve control of the particle’s position. Active video tracking based feedback control is implemented, which is able to work at a speed of up to 1 kHz, yielding good maneuverability of the magnetic beads.

36 MATERIALS SCIENCE↗

Highly non-linear solid core photonic crystal fiber with one nano hole

The numerical study of newly designed solid core photonic crystal fiber (SCPCF) having three hexagonal air hole rings in cladding region and one small nano hole at the center are presented. By using full vectorial finite element method (FV-FEM), we analyses the optical properties like effective area, nonlinearity and confinement loss of the proposed PCF. Results show that the change in core diameter controls the effective area, nonlinearity and confinement loss. A low effective area (3.34 µm{sup 2}), high nonlinearity (36.34 W{sup −1}km{sup −1}) and low confinement loss (0.00106 dB/km) are achieved at the communication wavelength 1.55 µm for the SCPCF having core air hole diameter 0.10 µm, cladding air holes diameter 1.00 µm and pitch 2.50 µm. This type of PCF is very useful in non-linear applications such as supercontinuum generation, four wave mixing, second harmonic generation etc.

36 MATERIALS SCIENCE↗

SU-F-207-05: Excess Heat Corrections in a Prototype Calorimeter for Direct Realization of CT Absorbed Dose to Phantom

Purpose: To reconcile air kerma and calorimetry measurements in a prototype calorimeter for obtaining absorbed dose in diagnostic CT beams. While corrections for thermal artifacts are routine and generally small in calorimetry of radiotherapy beams, large differences in relative stopping powers of calorimeter materials at the lower energies typical of CT beams greatly magnify their effects. Work-to-date on the problem attempts to reconcile laboratory measurements with modeling output from Monte Carlo and finite-element analysis of heat transfer. Methods: Small thermistor beads were embedded in a polystyrene (PS) core element of 1 cm diameter, which was inserted into a cylindrical HDPE phantom of 30 cm diameter and subjected to radiation in a diagnostic CT x-ray imaging system. Resistance changes in the thermistors due to radiation heating were monitored via lock-in amplifier. Multiple 3-second exposures were recorded at 8 different dose-rates from the CT system, and least-squares fits to experimental data were compared to an expected thermal response obtained by finite-element analysis incorporating source terms based on semi-empirical modeling and Monte Carlo simulation. Results: Experimental waveforms exhibited large thermal artifacts with fast time constants, associated with excess heat in wires and glass, and smaller steps attributable to radiation heating of the core material. Preliminary finite-element analysis follows the transient component of the signal qualitatively, but predicts a slower decay of temperature spikes. This was supplemented by non-linear least-squares fits incorporating semi-empirical formulae for heat transfer, which were used to obtain dose-to-PS in reasonable agreement with the output of Monte Carlo calculations that converts air kerma to absorbed dose. Conclusion: Discrepancies between the finite-element analysis and our experimental data testify to the very significant heat transfer correction required for absorbed dose calorimetry of diagnostic CT beams. The results obtained here are being used to refine both simulations and design of calorimeter core components.

60 APPLIED LIFE SCIENCES↗

Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake

We present an implementation of the trimmed serendipity finite element family, using the open-source finite element package Firedrake. The new elements can be used seamlessly within the software suite for problems requiring H 1 , H (curl), or H (div)-conforming elements on meshes of squares or cubes. To test how well trimmed serendipity elements perform in comparison to traditional tensor product elements, we perform a sequence of numerical experiments including the primal Poisson, mixed Poisson, and Maxwell cavity eigenvalue problems. Overall, we find that the trimmed serendipity elements converge, as expected, at the same rate as the respective tensor product elements, while being able to offer significant savings in the time or memory required to solve certain problems.

97 MATHEMATICS AND COMPUTING↗

NDT System for Metal Components in Concrete Structures (Final Report)

Steel reinforcements embedded within concrete can corrode and crack, leading to weakening of the structures, and existing NDT (non-destructive testing) techniques do not provide the full picture. Condition assessment is critical in evaluating these structures in order to ensure safe, long-term operation of the nuclear power plants. Improved NDT techniques are needed as the nation’s generating stations age and require action based on increasingly critical inspection data. The power industry uses eddy current test (ECT) during in-service inspections to detect and monitor defects such as cracks and corrosion in metals, particularly metal pipes. However, the detection of defects in the reinforcing steel embedded in concrete is far more challenging for numerous reasons. Primary among them is the concrete layer’s thickness, which prevents the ability to have a close proximity between sensor and metallic sample. One solution to this problem is to create a higher sensitivity technique which can inspect at depth, with good spatial resolution and excellent directional sensitivity, to isolate the metal buried deep in the concrete and characterize defects in the metal. The goal of the phase II research program was to study and develop a new reinforced concrete NDT technology based on anisotropic magnetoresistive (AMR) sensors designed specifically for ECT of steel reinforcements in concrete. The first technical objective was to demonstrate the capability of inspecting steel reinforcement structures, including metal rebar and tensioning cable at or below 6” of depth embedded in concrete. Another objective was to be able to confidently identify multiple layers of reinforcements at varying depths. In addition, the technique needed to be able to provide condition assessment of the metal, providing data on the structure and positioning of the steel members, material loss, and detection of the presence of breaks. An important part of the research and development was aimed at achieving superior performance compared to existing technology. The ability to detect corrosion breaks in unbonded multi-wire and multi-strand tendons was another important objective. The final objective that led to a successful program was to build a complete prototype portable scanning system capable of demonstrating the probe performance in the field. All of these objectives were met, which provided data for the system development work going forward. RMD worked with the engineering firm Simpson Gumpertz & Heger to develop a detailed problem definition for concrete structures and the necessary sensor specifications. In addition, we developed finite element simulation models for the eddy current based NDT system through the analysis of the electromagnetic (EM) properties of sample materials and the orientation of the transmitter, sensor array (receivers), metal, and intervening materials like concrete and air. Based on the modeling and specifications, we designed and fabricated prototype sensor modules. We then acquired and fabricated test samples to characterize and optimize the sensors. Finally, we built a complete prototype for testing on actual concrete structures. This new NDT technology has high promise for greatly improving capabilities in the inspection of steel reinforcements within concrete structures, such as rebar, liners, anchors, and prestressing cables. This method could be valuable in the maintenance of nuclear power plants, and many other structures critical to our nation’s infrastructure.

42 ENGINEERING↗

Space-Time Finite Element Tensor Network Approach for the Time-Dependent Convection–Diffusion–Reaction Equation with Variable Coefficients

In this paper, we present a new space-time Galerkin-like method, where we treat the discretization of spatial and temporal domains simultaneously. This method utilizes a mixed formulation of the tensor-train (TT) and quantized tensor-train (QTT) (please see Section Tensor-Train Decomposition), designed for the finite element discretization (Q1-FEM) of the time-dependent convection–diffusion–reaction (CDR) equation. We reformulate the assembly process of the finite element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the finite element operators. Recognizing the banded structure inherent in the finite element framework’s discrete operators, we further exploit the QTT format of the CDR to achieve greater speed and compression. Additionally, we present a comprehensive approach for integrating variable coefficients of CDR into the global discrete operators within the TT/QTT framework. The effectiveness of the proposed method, in terms of memory efficiency and computational complexity, is demonstrated through a series of numerical experiments, including a semi-linear example.

convection–diffusion–reaction equation↗

Finite-element solution for a combined radiative-conductive analysis with mixed diffuse-specular surface characteristics

The finite-element method has been applied to solve a combined radiative-conductive heat transfer problem for a large space telescope similar to those used in orbiting satellites. The derivation of the underlying matrices and associated solution algorithm for a 2-D triangular element is presented in detail. The resulting expressions for this triangular element typify such an analysis, which yields constitutive matrices when the heat equation is cast in the matrix form. The relevant matrices include those pertaining to thermal conductance, internal heat generation, radiative exchanges, and all possible external thermal loadings. Emphasis is placed on the treatment of non-linear radiative interchange between surfaces in an enclosure having mixed diffuse-specular surface characteristics. Essential differences in governing equations describing these distinctive surface characteristics are identified. Concluding remarks are drawn from an example simulating a Cassegrainian space telescope.

Lee, H.-P.↗

Three-dimensional modelling in magnetotelluric and magnetic variational sounding

The Galerkin finite-element method is used to obtain approximate solutions for the three-dimensional induction problem. A rectangular conductive prism is considered as an example, and solutions are obtained for linear and circularly polarized incident plane-wave fields. Magnetotelluric tensor impedances and magnetic transfer functions are computed. Polar diagrams of the tensor impedances and magnetic transfer functions along with their amplitude contour maps are presented. The dimensionality parameter, skew, is contoured at the surface of the earth. It is shown that the relative amplitudes and shapes of the additional and principal impedance polar diagrams can be used to determine the dimensionality of geoelectrical structures. Stations with skew values greater than 0.2 are significantly influenced by the three-dimensionality of the geoelectric structure. The amplitudes of the magnetic transfer function and the orientations of its polar diagrams exhibit large anomalies in the vicinity of the intersection of the lateral contacts.

Reddy, I. K.↗