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Meshless Local Petrov-Galerkin (MLPG) Method with Orthogonal Polynomials for Euler-Bernoulli Beam Problems

In this paper, the feasibility of orthogonal polynomials in the meshless local Petrov Galerkin method (MLPG) method is studied. The orthogonal polynomials, Chebyshev and Legendre polynomials, are used in this MLPG method as trial functions. The test functions used were power functions with smooth derivatives at their ends. The performance of these methods is studied by applying these methods to Euler-Bernoulli beam problems. The MLPG-Galerkin and Legendre methods passed all the patch tests for simple beam problems. Next the formulations are tested on complex beam problems such as beams with partial loadings and continuous beam problems. Problems with load discontinuities and additional supports require special attention. Near discontinuities, judicious choice of number of nodes and nodal placements are needed to obtain accurate deflections, slopes, moments and shear forces. As polynomial functions are used, the large number of nodes can create a transformation matrix that is ill-conditioned, resulting in problems with the inversion of the matrix. The conditioning worsens as the number of nodes are increased beyond 20. Quadruple precision was needed for models to obtain accurate solutions. Even with quadruple precision the accuracy of the method suffers as the number of nodes is increased beyond 20. This appears to be a drawback of the MLPG-Chebyshev and MLPG-Legendre methods.

Raju, Ivatury S.

A Meshless Local Petrov-Galerkin Method for Euler-Bernoulli Beam Problems

An accurate and yet simple Meshless Local Petrov-Galerkin (MLPG) formulation for analyzing beam problems is presented. In the formulation, simple weight functions are chosen as test functions. The use of these functions shows that the weak form can be integrated with conventional Gaussian integration. The MLPG method was evaluated by applying the formulation to a variety of patch test and thin beam problems. The formulation successfully reproduced exact solutions to machine accuracy when test functions with C2 continuity and an appropriate order of basis functions are used.

Raju, I. S.

Dynamic analysis of the GEOS satellite

The assumed modes method is used to investigate the stability of the GEOS satellite. The system is discretized by representing the continuous displacement by finite series of space-dependent admissible functions multiplied by time-dependent generalized coordinates. The spatial dependence is eliminated by integration over the elastic domains, so that the testing functional reduces to a testing function. The sign properties of the testing function are then tested and the equilibrium defined as nontrivial. In considering the stability of small motions about nontrivial equilibrium, it is shown that if the analysis performed by ignoring the motion of the mass center indicates stability, then the system remains stable if the motion of the mass center is included.

Meirovitch, L.

HAL/S-360 compiler test activity report

The levels of testing employed in verifying the HAL/S-360 compiler were as follows: (1) typical applications program case testing; (2) functional testing of the compiler system and its generated code; and (3) machine oriented testing of compiler implementation on operational computers. Details of the initial test plan and subsequent adaptation are reported, along with complete test results for each phase which examined the production of object codes for every possible source statement.

Helmers, C. T.

Electrical Evaluation of RCA MWS5501D Random Access Memory, Volume 2, Appendix a

The electrical characterization and qualification test results are presented for the RCA MWS5001D random access memory. The tests included functional tests, AC and DC parametric tests, AC parametric worst-case pattern selection test, determination of worst-case transition for setup and hold times, and a series of schmoo plots. The address access time, address readout time, the data hold time, and the data setup time are some of the results surveyed.

Klute, A.

Electrical Evaluation of RCA MWS5001D Random Access Memory, Volume 3, Appendix B

The electrical characterization and qualification test results are presented for the RCA MWS5001D random access memory. The tests included functional tests, AC and DC parametric tests, AC parametric worst-case pattern selection test, determination of worst-case transition for setup and hold times, and a series of schmoo plots. The test values for the output voltage, average input current, the supply current and the leakage current are presented.

Klute, A.

Electrical Evaluation of RCA MWS5001D Random Access Memory, Volume 4, Appendix C

The electrical characterization and qualification test results are presented for the RCA MWS5001D random access memory. The tests included functional tests, AC and DC parametric tests, AC parametric worst-case pattern selection test, determination of worst-case transition for setup and hold times, and a series of schmoo plots. Statistical analysis data is supplied along with write pulse width, read cycle time, write cycle time, and chip enable time data.

Klute, A.

Electrical Evaluation of RCA MWS5001D Random Access Memory, Volume 5, Appendix D

The electrical characterization and qualification test results are presented for the RCA MWS 5001D random access memory. The tests included functional tests, AC and DC parametric tests, AC parametric worst-case pattern selection test, determination of worst-case transition for setup and hold times, and a series of schmoo plots. Average input high current, worst case input high current, output low current, and data setup time are some of the results presented.

Klute, A.

Qualification of UHF Antenna for Extreme Martian Thermal Environments

The purpose of this development was to validate the use of the external Rover Ultra High Frequency (RUHF) antenna for space under extreme thermal environments to be encountered during the surface operations of the Mars Science Laboratory (MSL) mission. The antenna must survive all ground operations plus the nominal 670 Martian sol mission that includes summer and winter seasons of the Mars thermal environment.The qualification effort was to verify that the RUHF antenna design and its bonding and packaging processes are adequate to survive the harsh environmental conditions. The RUHF is a quadrifilar helix antenna mounted on the MSL Curiosity rover deck. The main components of the RUHF antenna are the helix structure, feed cables, and hybrid coupler, and the high-power termination load. In the case of MSL rover externally mounted hardware, not only are the expected thermal cycle depths severe, but there are temperature offsets between the Mars summer and winter seasons. The total number of temperature cycles needed to be split into two regimes of summer cycles and winter cycles. The qualification test was designed to demonstrate a survival life of three times more than all expected ground testing, plus a nominal 670 Martian sol missions. Baseline RF tests and a visual inspection were performed prior to the start of the qualification test. Functional RF tests were performed intermittently during chamber breaks over the course of the qualification test. For the RF return loss measurements, the antenna was tested in a controlled environment outside the thermal chamber with a vector network analyzer that was calibrated over the antenna s operational frequency range. A total of 2,010 thermal cycles were performed. Visual inspection showed a dulling of the solder material. This change will not affect the performance of the antenna. No other changes were observed. RF tests were performed on the RUHF helix antenna, hybrid, and load after the 2,010 qualification cycles test. The RF performance of the RUHF antenna, hybrid, and load were almost identical before and after the complete test. Therefore, the developed design of RUHF is qualified for a long-duration MSL mission. The RUHF antenna has not been used for long-duration missions such as MSL in the past. The state-of-the-art technology of the RUHF antenna is used to develop the antennas for MSL mission survivability. This developmental test data provides the confidence in using this RUHF antenna for future NASA missions to Mars.

Ramesham, Rajeshuni

Gradient Calculation Methods on Arbitrary Polyhedral Unstructured Meshes for Cell-Centered CFD Solvers

A survey of gradient reconstruction methods for cell-centered data on unstructured meshes is conducted within the scope of accuracy assessment. Formal order of accuracy, as well as error magnitudes for each of the studied methods, are evaluated on a complex mesh of various cell types through consecutive local scaling of an analytical test function. The tests highlighted several gradient operator choices that can consistently achieve 1st order accuracy regardless of cell type and shape. The tests further offered error comparisons for given cell types, leading to the observation that the "ideal" gradient operator choice is not universal. Practical implications of the results are explored via CFD solutions of a 2D inviscid standing vortex, portraying the discretization error properties. A relatively naive, yet largely unexplored, approach of local curvilinear stencil transformation exhibited surprisingly favorable properties

Meshes

Coupling Finite Element and Meshless Local Petrov-Galerkin Methods for Two-Dimensional Potential Problems

A coupled finite element (FE) method and meshless local Petrov-Galerkin (MLPG) method for analyzing two-dimensional potential problems is presented in this paper. The analysis domain is subdivided into two regions, a finite element (FE) region and a meshless (MM) region. A single weighted residual form is written for the entire domain. Independent trial and test functions are assumed in the FE and MM regions. A transition region is created between the two regions. The transition region blends the trial and test functions of the FE and MM regions. The trial function blending is achieved using a technique similar to the 'Coons patch' method that is widely used in computer-aided geometric design. The test function blending is achieved by using either FE or MM test functions on the nodes in the transition element. The technique was evaluated by applying the coupled method to two potential problems governed by the Poisson equation. The coupled method passed all the patch test problems and gave accurate solutions for the problems studied.

Chen, T.

Functional Flight Test Report for Positive Systems' ADAR System 5500 Sensor SN8 Linear

This report describes results of the functional flight test conducted with the Positive Systems' ADAR 5500 sensor system (serial number 8, linear configuration) near Winslow, Arizona on June 30 and July 1, 1999. The in-flight test is one component of the NASA Scientific Data Purchase (SDP) Validation and Verification (V&V) process. It allows to measure characteristics of the entire sensor system affected by both performance of the sensor during a flight and post-flight image processing. The following characteristics were analyzed: changes of dark digital numbers (DN's), radiometric linearity, signal-to-noise ratio (SNR), spatial resolution, and geolocation accuracy. The measured characteristics were compared with the image product specifications defined in the Positive Systems' SDP contract. Dependence of the dark DN's on several factors was analyzed, but no significant correlation was found. However, the observed changes in dark DN's were relatively small, which justifies usage of a constant value in the dark DN subtraction procedure during post-processing. Dependence of measured at-sensor, in-band radiance (in arbitrary units) on measured in-band ground reflectance is very well described by a linear function - The sensor fulfills the linearity requirement. Measured SNR values lower than the contract specifications, but accuracy of that test was possibly affected by non-uniformity of the employed gray-scale panels. The SNR values are generally sufficiently high for most applications. SNR can also be improved during standard flights by using longer exposure times. Full width at half maximum (FWHM) of an edge response derived line spread function was used as a measure of spatial resolution. FWHM was generally smaller than twice the ground sample distance (GSD), in agreement with the contract specifications. Accuracy of the geolocation information, which is provided for the particular images in a metadata file, was found to meet contract requirements as well.

Stanley, Tom

Spaceflight-Induced Cardiovascular Changes and Recovery During NASA's Functional Task Test

Microgravity-induced physiological changes could impair a crewmember s performance upon return to a gravity environment. The Functional Task Test (FTT) is designed to correlate these physiological changes to performance in mission-critical tasks. The Recovery from Fall/Stand Test (RFST) simulates one such task, measuring the ability to recover from a prone position and the cardiovascular response to orthostasis. The purpose of this study was to evaluate spaceflight-induced cardiovascular changes during the FTT. METHODS: Five astronauts participated in the FTT before 10-15 day missions, on landing day (R+0), and one (R+1), six (R+6) and thirty (R+30) days after landing. The RFST consisted of a 2-minute prone rest followed by a 3-minute stand during which heart rate (HR, Holter) and continuous blood pressure (BP, Finometer) were measured. Spectral heart rate variability (HRV) was calculated during the RFST to approximate autonomic function. Statistical analysis was performed with two-factor repeated measures ANOVA. RESULTS: During RFST, HR was higher on R+0 than preflight (p<0.004). This increase in HR persisted on R+1 and R+6 during the stand portion of RFST (p<0.026). BP was well-regulated on all test days. Parasympathetic activity was diminished on R+0 (p=0.035). Sympathovagal balance tended to be affected by spaceflight (main effect, p=0.072), appearing to be slightly elevated during postflight RFST except on R+30. Additionally, analysis of HR during the functional tasks yielded a higher HR on R+0 than preflight during 8 of 11 tasks analyzed, where all tasks had HR return to preflight values by R+30 (p<0.05). CONCLUSION: Spaceflight causes an increase in HR, decrease in parasympathetic activity, and increase in sympathovagal balance, which we confirmed during RFST. These spaceflight-induced changes seen in the RFST, along with the increased postflight HR in most functional tasks, can be used to assess functional performance after short-duration spaceflight.

Arzeno, N. M.

Identification of Differential Equations by Dynamics-Guided Weighted Weak Form with Voting

In the identification of differential equations from data, significant progresses have been made with the weak/integral formulation. In this paper, we explore the direction of finding more efficient and robust test functions adaptively given the observed data. While this is a difficult task, we propose weighting a collection of localized test functions for better identification of differential equations from a single trajectory of noisy observations on the differential equation. We find that using high dynamic regions is effective in finding the equation as well as the coefficients, and propose a dynamics indicator per differential term and weight the weak form accordingly. For stable identification against noise, we further introduce a voting strategy to identify the active features from an ensemble of recovered results by selecting the features that frequently occur in different weighting of test functions. Systematic numerical experiments are provided to demonstrate the robustness of our method.

97 MATHEMATICS AND COMPUTING

Discontinuous dual-primal mixed finite elements for elliptic problems

We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

Bottasso, Carlo L.

Ultimate Tensile Strength as a Function of Test Rate for Various Ceramic Matrix Composites at Elevated Temperatures

Ultimate tensile strength of five different continuous fiber-reinforced ceramic composites, including SiC/BSAS (2D 2 types), SiC/MAS-5 (2D), SiC/SiC (2D enhanced), and C/SiC(2D) was determined as a function of test rate at I 100 to 1200 'C in air. All five composite materials exhibited a significant dependency of ultimate strength on test rate such that the ultimate strength decreased with decreasing test rate, similar to the behavior observed in many advanced monolithic ceramics at elevated temperatures. The application of the preloading technique as well as the prediction of life from one loading configuration (constant stress rate) to another (constant stress loading) for SiC/BSAS suggested that the overall macroscopic failure mechanism of the composites would be the one governed by a power-law type of damage evolution/accumulation, analogous to slow crack growth commonly observed in advanced monolithic ceramics.

Choi, Sung R.

Comments on the MHD stability of coronal plasmas with line-tying

Reasonable boundary conditions and test functions for photospheric line-tying are discussed, and their effects on the ideal MHD stability of coronal loops are considered. It is concluded that the plasma at the footpoints of a loop may safely be assumed to be stationary. When a simple perturbed test function is used for the energy principle, the function should be helical in form. Constraints on the test function should be discarded because they overestimate stability.

An, C.-H.