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  • 1
    Electronic Resource
    Electronic Resource
    Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 313-320 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100406
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A simple local error estimator and an adaptive time-stepping procedure for direct integration method in dynamic analysis (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 273-292 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple a posteriori local error estimator for time discretization in structural dynamic analysis is presented. It is derived from the difference of the solutions between an ordinary integration method (the Newmark scheme) and another higher-order one which assumes that the derivatives of accelerations vary linearly within each time step. It may be obtained directly without resolving new equations, so the additional computational cost is small and the implementation is convenient. Furthermore, it is shown that this error estimator may also be obtained by Taylor expansion or by a post-processing technique. Accordingly, an adaptive time-stepping procedure, which automatically adjusts the time-step size so that the local error at each time step is within a prescribed accuracy, is described. Numerical examples, including two single-DOF problems, a two-DOF problem and a multi-DOF model, are presented. The results show that the presented local error estimator is simple, reliable and accurate.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090402
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A postprocessed error estimate and an adaptive procedure for the semidiscrete finite element method in dynamic analysis (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3585-3603 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we present a postprocessed type of a posteriori error estimate and a h-version adaptive procedure for the semidiscrete finite element method in dynamic analysis. In space the super-convergent patch recovery technique is used for determining higher-order accurate stresses and, thus, a spatial error estimate. In time a postprocessing technique is developed for obtaining a local error estimate for one step time integration schemes (the HHT-α method). Coupling the error estimate with a mesh generator, a h-version adaptive finite element procedure is presented for two-dimensional dynamic analysis. It updates the spatial mesh and time step automatically so that the discretization errors are controlled within specified tolerances. Numerical studies on different problems are presented for demonstrating the performances of the proposed adaptive procedure.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372102
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  • 4
    Electronic Resource
    Electronic Resource
    STRUCTURAL DYNAMIC ANALYSIS BY A TIME-DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2131-2152 
    Details
    ISSN: 0029-5981
    Keywords: discontinuous Galerkin finite element method ; predictor-multicorrector ; adaptive time integration ; structural dynamics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper studies a time-discontinuous Galerkin finite element method for structural dynamic problems, by which both displacements and velocities are approximated as piecewise linear functions in the time domain and may be discontinuous at the discrete time levels. A new iterative solution algorithm which involves only one factorization for each fixed time step size and a few iterations at each step is presented for solving the resulted system of coupled equations. By using the jumps of the displacements and the velocities in the total energy norm as error indicators, an adaptive time-stepping procedure for selecting the proper time step size is described. Numerical examples including both single-DOF and multi-DOF problems are used to illustrate the performance of these algorithms. Comparisons with the exact results and/or the results by the Newmark integration scheme are given. It is shown that the time-discontinuous Galerkin finite element method discussed in this study possesses good accuracy (third order) and stability properties, its numerical implementation is not difficult, and the higher computational cost needed in each time step is compensated by use of a larger time step size.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    FINITE ELEMENT METHOD FOR GRADIENT PLASTICITY AT LARGE STRAINS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 619-633 
    Details
    ISSN: 0029-5981
    Keywords: gradient plasticity ; strain localization ; mixed strain element method ; large strain ; consistent algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method for gradient elasto-plastic continuum in which the yield strength of strain hardening/softening materials not only depends on the effective plastic strain but also on its Laplacian is presented. The consistent integration algorithm to update the stress and the internal state variable at integration points and the consistent compliance matrix for the gradient plasticity are formulated in the non-local sense.The methodology to derive the finite element formulation for the gradient plasticity at large strains presented in this paper is applicable to general finite element analysis; the formulation in the context of the two-dimensional four-noded mixed finite element with one integration point and mean von Mises yield criterion is particularly derived.Numerical examples are tested to demonstrate the capability and performance of the present finite element method at large strain in solving for the strain localization problem.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 6
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    Two-Step Resonance-Enhanced Desorption Laser Mass Spectrometry for In Situ Analysis of Organic-Rich Environments (2016)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: A wide diversity of planetary surfaces in the solar system represent high priority targets for in situ compositional and contextual analysis as part of future missions. The planned mission portfolio will inform our knowledge of the chemistry at play on Mars, icy moons, comets, and primitive asteroids, which can lead to advances in our understanding of the interplay between inorganic and organic building blocks that led to the evolution of habitable environments on Earth and beyond. In many of these environments, the presence of water or aqueously altered mineralogy is an important indicator of habitable environments that are present or may have been present in the past. As a result, the search for complex organic chemistry that may imply the presence of a feedstock, if not an inventory of biosignatures, is naturally aligned with targeted analyses of water-rich surface materials. Here we describe the two-step laser mass spectrometry (L2MS) analytical technique that has seen broad application in the study of organics in meteoritic samples, now demonstrated to be compatible with an in situ investigation with technique improvements to target high priority planetary environments as part of a future scientific payload. An ultraviolet (UV) pulsed laser is used in previous and current embodiments of laser desorption/ionization mass spectrometry (LDMS) to produce ionized species traceable to the mineral and organic composition of a planetary surface sample. L2MS, an advanced technique in laser mass spectrometry, is selective to the aromatic organic fraction of a complex sample, which can provide additional sensitivity and confidence in the detection of specific compound structures. Use of a compact two-step laser mass spectrometer prototype has been previously reported to provide specificity to key aromatic species, such as PAHs, nucleobases, and certain amino acids. Recent improvements in this technique have focused on the interaction between the mineral matrix and the organic analyte. The majority of planetary targets of astrobiological interest are characterized by the presence of water or hydrated mineral phases. Water signatures can indicate a history of available liquid water that may have played an important role in the chemical environment of these planetary surfaces and subsurfaces. The studies we report here investigate the influence of water content on the detectability of organics by L2MS in planetary analog samples.
    Keywords: Lunar and Planetary Science and Exploration
    Type: GSFC-E-DAA-TN29318 , Lunar and Planetary Science Conference; Mar 21, 2016 - Mar 25, 2016; The Woodlands, TX; United States
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  • 7
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    It's a Trap! A Review of MOMA and Other Ion Traps in Space or Under Development (2014)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: Since the Viking Program, quadrupole mass spectrometer (QMS) instruments have been used to explore a wide survey of planetary targets in our solar system, including (from the inner to outer reaches): Venus (Pioneer); our moon (LADEE); Mars (Viking, Phoenix, and Mars Science Laboratory); and, Saturns largest moon Titan (Cassini-Huygens). More recently, however, ion trap mass spectrometer (ITMS) instruments have found a niche as smaller, versatile alternatives to traditional quadrupole mass analyzers, capable of in situ characterization of planetary environments and the search for organic matter. For example, whereas typical QMS systems are limited to a mass range up to 500 Da and normally require multiple RF frequencies and pressures of less than 10(exp -6) mbar for optimal operation, ITMS instruments commonly reach upwards of 1000 Da or more on a single RF frequency, and function in higher pressure environments up to 10(exp -3) mbar.
    Keywords: Lunar and Planetary Science and Exploration
    Type: GSFC-E-DAA-TN18368 , International Workshop on Instrumentation for Planetary Missions (IPM-2014); Nov 04, 2014 - Nov 07, 2014; Greenbelt, MD; United States
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  • 8
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    Precision Subsampling System for Mars Surface Missions (2012)
    In:  CASI
    Details
    Publication Date: 2019-08-13
    Description: The ability to analyze heterogeneous rock samples at fine spatial scales would represent a powerful addition to our planetary in situ analytical toolbox. This is particularly true for Mars, where the signatures of past environments and, potentially, habitability are preserved in chemical and morphological variations across sedimentary layers and among mineral pr.ases in a given rock specimen. On Earth, microbial life often associates with surfaces at the interface of chemical nutrients, and ultimately retains sub-millimeter to millimeter-scale layer confinement in fossilization. On Mars, and possibly other bodies, trace chemical markers (elemental, organic/molecular, isotopic, chiral, etc.) and fine-scale morphological markers (e.g., micro-fossils) may he too subtle, degraded, or ambiguous to be detected, using miniaturized instrumentation, without some concentration or isolation. This is because (i) instrument sensitivity may not be high enough to detect trace markers in bulk averages; and (ii) instrument s~lectiviry may not be sufficient to distinguish such markers from interfering/counteracting signals from the bulk. Moreover from a fundamental chemostratigraphic perspective there would be a great benefit to assessing specific chemical and stable isotopic gradients, over millimeter-to-centimeter scales and beyond, with higher precision than currently possible in situ. We have developed a precision subsampling system (PSS) that addresses this need while remaining relatively flexible to a variety of instruments that may take advantage of the capability on future missions. The PSS is relevant to a number of possible lander/rover missions, especially Mars Sample Return. Our specific PSS prototype is undergoing testing under Mars ambient conditions, on a variety of natural analog rocks and rock drill cores, using a set of complementary flight-compatible measurement techniques. The system is available for testing with other contact instruments that may benefit from precision sampling.
    Keywords: Lunar and Planetary Science and Exploration
    Type: GSFC.CPR.6531.2012 , GSFC.CPR.6532.2012 , Concepts and Approaches for Mars Exploration; Jun 12, 2012 - Jun 14, 2012; Houston, TX; United States
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  • 9
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    Development of a Linear Ion Trap Mass Spectrometer (LITMS) Investigation for Future Planetary Surface Missions (2014)
    In:  CASI
    Details
    Publication Date: 2019-08-13
    Description: Future surface missions to Mars and other planetary bodies will benefit from continued advances in miniature sensor and sample handling technologies that enable high-performance chemical analyses of natural samples. Fine-scale (approx.1 mm and below) analyses of rock surfaces and interiors, such as exposed on a drill core, will permit (1) the detection of habitability markers including complex organics in association with their original depositional environment, and (2) the characterization of successive layers and gradients that can reveal the time-evolution of those environments. In particular, if broad-based and highly-sensitive mass spectrometry techniques could be brought to such scales, the resulting planetary science capability would be truly powerful. The Linear Ion Trap Mass Spectrometer (LITMS) investigation is designed to conduct fine-scale organic and inorganic analyses of short (approx.5-10 cm) rock cores such as could be acquired by a planetary lander or rover arm-based drill. LITMS combines both pyrolysis/gas chromatograph mass spectrometry (GCMS) of sub-sampled core fines, and laser desorption mass spectrometry (LDMS) of the intact core surface, using a common mass analyzer, enhanced from the design used in the Mars Organic Molecule Analyzer (MOMA) instrument on the 2018 ExoMars rover. LITMS additionally features developments based on the Sample Analysis at Mars (SAM) investigation on MSL and recent NASA-funded prototype efforts in laser mass spectrometry, pyrolysis, and precision subsampling. LITMS brings these combined capabilities to achieve its four measurement objectives: (1) Organics: Broad Survey Detect organic molecules over a wide range of molecular weight, volatility, electronegativity, concentration, and host mineralogy. (2) Organic: Molecular Structure Characterize internal molecular structure to identify individual compounds, and reveal functionalization and processing. (3) Inorganic Host Environment Assess the local chemical/mineralogical makeup of organic host phases to help determine deposition and preservation factors. (4) Chemical Stratigraphy Analyze the fine spatial distribution and variation of key species with depth.
    Keywords: Lunar and Planetary Science and Exploration
    Type: GSFC-E-DAA-TN17854 , International Workshop on Instrumentation for Planetary Missions; Nov 04, 2014 - Nov 07, 2014; Greenbelt, MD; United States
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  • 10
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    Laser Time-of-Flight Mass Spectrometry for Future In Situ Planetary Missions (2012)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: Laser desorption/ionization time-of-flight mass spectrometry (LD-TOF-MS) is a versatile, low-complexity instrument class that holds significant promise for future landed in situ planetary missions that emphasize compositional analysis of surface materials. Here we describe a 5kg-class instrument that is capable of detecting and analyzing a variety of analytes directly from rock or ice samples. Through laboratory studies of a suite of representative samples, we show that detection and analysis of key mineral composition, small organics, and particularly, higher molecular weight organics are well suited to this instrument design. A mass range exceeding 100,000 Da has recently been demonstrated. We describe recent efforts in instrument prototype development and future directions that will enhance our analytical capabilities targeting organic mixtures on primitive and icy bodies. We present results on a series of standards, simulated mixtures, and meteoritic samples.
    Keywords: Lunar and Planetary Science and Exploration
    Type: GSFC.CPR.6830.2012 , Instrumentation for Planetary Missions Workshop/NASA; Oct 12, 2012; Greenbelt, MD; United States
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