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  • 1
    Publication Date: 2013-05-24
    Description: Innate lymphoid cells (ILCs) are a recently characterized family of immune cells that have critical roles in cytokine-mediated regulation of intestinal epithelial cell barrier integrity. Alterations in ILC responses are associated with multiple chronic human diseases, including inflammatory bowel disease, implicating a role for ILCs in disease pathogenesis. Owing to an inability to target ILCs selectively, experimental studies assessing ILC function have predominantly used mice lacking adaptive immune cells. However, in lymphocyte-sufficient hosts ILCs are vastly outnumbered by CD4(+) T cells, which express similar profiles of effector cytokines. Therefore, the function of ILCs in the presence of adaptive immunity and their potential to influence adaptive immune cell responses remain unknown. To test this, we used genetic or antibody-mediated depletion strategies to target murine ILCs in the presence of an adaptive immune system. We show that loss of retinoic-acid-receptor-related orphan receptor-gammat-positive (RORgammat(+)) ILCs was associated with dysregulated adaptive immune cell responses against commensal bacteria and low-grade systemic inflammation. Remarkably, ILC-mediated regulation of adaptive immune cells occurred independently of interleukin (IL)-17A, IL-22 or IL-23. Genome-wide transcriptional profiling and functional analyses revealed that RORgammat(+) ILCs express major histocompatibility complex class II (MHCII) and can process and present antigen. However, rather than inducing T-cell proliferation, ILCs acted to limit commensal bacteria-specific CD4(+) T-cell responses. Consistent with this, selective deletion of MHCII in murine RORgammat(+) ILCs resulted in dysregulated commensal bacteria-dependent CD4(+) T-cell responses that promoted spontaneous intestinal inflammation. These data identify that ILCs maintain intestinal homeostasis through MHCII-dependent interactions with CD4(+) T cells that limit pathological adaptive immune cell responses to commensal bacteria.〈br /〉〈br /〉〈a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3699860/" target="_blank"〉〈img src="https://static.pubmed.gov/portal/portal3rc.fcgi/4089621/img/3977009" border="0"〉〈/a〉   〈a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3699860/" target="_blank"〉This paper as free author manuscript - peer-reviewed and accepted for publication〈/a〉〈br /〉〈br /〉〈span class="detail_caption"〉Notes: 〈/span〉Hepworth, Matthew R -- Monticelli, Laurel A -- Fung, Thomas C -- Ziegler, Carly G K -- Grunberg, Stephanie -- Sinha, Rohini -- Mantegazza, Adriana R -- Ma, Hak-Ling -- Crawford, Alison -- Angelosanto, Jill M -- Wherry, E John -- Koni, Pandelakis A -- Bushman, Frederic D -- Elson, Charles O -- Eberl, Gerard -- Artis, David -- Sonnenberg, Gregory F -- 2-P30 CA016520/CA/NCI NIH HHS/ -- AI061570/AI/NIAID NIH HHS/ -- AI074878/AI/NIAID NIH HHS/ -- AI087990/AI/NIAID NIH HHS/ -- AI095466/AI/NIAID NIH HHS/ -- AI095608/AI/NIAID NIH HHS/ -- AI095776/AI/NIAID NIH HHS/ -- AI097333/AI/NIAID NIH HHS/ -- AI102942/AI/NIAID NIH HHS/ -- DK071176/DK/NIDDK NIH HHS/ -- DP5 OD012116/OD/NIH HHS/ -- DP5OD012116/OD/NIH HHS/ -- P01 DK071176/DK/NIDDK NIH HHS/ -- P30 DK050306/DK/NIDDK NIH HHS/ -- P30DK50306/DK/NIDDK NIH HHS/ -- R01 AI061570/AI/NIAID NIH HHS/ -- R01 AI074878/AI/NIAID NIH HHS/ -- R01 AI095466/AI/NIAID NIH HHS/ -- R01 AI097333/AI/NIAID NIH HHS/ -- R01 AI102942/AI/NIAID NIH HHS/ -- R21 AI083480/AI/NIAID NIH HHS/ -- R21 AI087990/AI/NIAID NIH HHS/ -- T32 AI007532/AI/NIAID NIH HHS/ -- T32 AI055428/AI/NIAID NIH HHS/ -- T32-AI055428/AI/NIAID NIH HHS/ -- U01 AI095608/AI/NIAID NIH HHS/ -- England -- Nature. 2013 Jun 6;498(7452):113-7. doi: 10.1038/nature12240. Epub 2013 May 22.〈br /〉〈span class="detail_caption"〉Author address: 〈/span〉Division of Gastroenterology, Department of Medicine, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.〈br /〉〈span class="detail_caption"〉Record origin:〈/span〉 〈a href="http://www.ncbi.nlm.nih.gov/pubmed/23698371" target="_blank"〉PubMed〈/a〉
    Keywords: Animals ; Antigen Presentation/immunology ; Bacteria/*immunology ; CD4-Positive T-Lymphocytes/cytology/*immunology/pathology ; Cell Proliferation ; Histocompatibility Antigens Class II/immunology/metabolism ; Humans ; Immunity, Innate/*immunology ; Inflammation/pathology ; Interleukin-17/metabolism ; Interleukin-23/metabolism ; Interleukins/metabolism ; Intestines/*immunology/*microbiology/pathology ; Mice ; Mice, Inbred C57BL ; Mice, Transgenic ; Nuclear Receptor Subfamily 1, Group F, Member 3/metabolism ; *Symbiosis
    Print ISSN: 0028-0836
    Electronic ISSN: 1476-4687
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
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  • 2
    Publication Date: 2012-06-08
    Description: The mammalian intestinal tract is colonized by trillions of beneficial commensal bacteria that are anatomically restricted to specific niches. However, the mechanisms that regulate anatomical containment remain unclear. Here, we show that interleukin-22 (IL-22)-producing innate lymphoid cells (ILCs) are present in intestinal tissues of healthy mammals. Depletion of ILCs resulted in peripheral dissemination of commensal bacteria and systemic inflammation, which was prevented by administration of IL-22. Disseminating bacteria were identified as Alcaligenes species originating from host lymphoid tissues. Alcaligenes was sufficient to promote systemic inflammation after ILC depletion in mice, and Alcaligenes-specific systemic immune responses were associated with Crohn's disease and progressive hepatitis C virus infection in patients. Collectively, these data indicate that ILCs regulate selective containment of lymphoid-resident bacteria to prevent systemic inflammation associated with chronic diseases.〈br /〉〈br /〉〈a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3659421/" target="_blank"〉〈img src="https://static.pubmed.gov/portal/portal3rc.fcgi/4089621/img/3977009" border="0"〉〈/a〉   〈a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3659421/" target="_blank"〉This paper as free author manuscript - peer-reviewed and accepted for publication〈/a〉〈br /〉〈br /〉〈span class="detail_caption"〉Notes: 〈/span〉Sonnenberg, Gregory F -- Monticelli, Laurel A -- Alenghat, Theresa -- Fung, Thomas C -- Hutnick, Natalie A -- Kunisawa, Jun -- Shibata, Naoko -- Grunberg, Stephanie -- Sinha, Rohini -- Zahm, Adam M -- Tardif, Melanie R -- Sathaliyawala, Taheri -- Kubota, Masaru -- Farber, Donna L -- Collman, Ronald G -- Shaked, Abraham -- Fouser, Lynette A -- Weiner, David B -- Tessier, Philippe A -- Friedman, Joshua R -- Kiyono, Hiroshi -- Bushman, Frederic D -- Chang, Kyong-Mi -- Artis, David -- 2-P30 CA016520/CA/NCI NIH HHS/ -- AI061570/AI/NIAID NIH HHS/ -- AI074878/AI/NIAID NIH HHS/ -- AI083480/AI/NIAID NIH HHS/ -- AI087990/AI/NIAID NIH HHS/ -- AI095466/AI/NIAID NIH HHS/ -- AI095608/AI/NIAID NIH HHS/ -- AI47619/AI/NIAID NIH HHS/ -- K08 DK093784/DK/NIDDK NIH HHS/ -- K08-DK093784/DK/NIDDK NIH HHS/ -- P30 AI 045008/AI/NIAID NIH HHS/ -- P30DK50306/DK/NIDDK NIH HHS/ -- R01 AI061570/AI/NIAID NIH HHS/ -- R01 AI074878/AI/NIAID NIH HHS/ -- R01 AI095466/AI/NIAID NIH HHS/ -- R01 AI102942/AI/NIAID NIH HHS/ -- R21 AI083480/AI/NIAID NIH HHS/ -- R21 AI087990/AI/NIAID NIH HHS/ -- T32 AI007532/AI/NIAID NIH HHS/ -- T32 AI055428/AI/NIAID NIH HHS/ -- T32 RR007063/RR/NCRR NIH HHS/ -- T32-AI007532/AI/NIAID NIH HHS/ -- T32-AI055428/AI/NIAID NIH HHS/ -- T32-RR007063/RR/NCRR NIH HHS/ -- U01 AI095608/AI/NIAID NIH HHS/ -- New York, N.Y. -- Science. 2012 Jun 8;336(6086):1321-5. doi: 10.1126/science.1222551. Epub 2012 Jun 6.〈br /〉〈span class="detail_caption"〉Author address: 〈/span〉Department of Microbiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA.〈br /〉〈span class="detail_caption"〉Record origin:〈/span〉 〈a href="http://www.ncbi.nlm.nih.gov/pubmed/22674331" target="_blank"〉PubMed〈/a〉
    Keywords: Adult ; Alcaligenes/immunology/isolation & purification/*physiology ; Animals ; Bacterial Translocation ; Crohn Disease/immunology/microbiology ; Hepatitis C, Chronic/immunology/microbiology ; Humans ; Immunity, Innate ; Inflammation ; Interleukins/administration & dosage/biosynthesis/*immunology ; Intestines/*immunology/microbiology ; Leukocyte L1 Antigen Complex/metabolism ; Liver/microbiology ; Lymph Nodes/immunology ; Lymphocytes/*immunology ; Lymphoid Tissue/*immunology/*microbiology ; Macaca mulatta ; Mice ; Mice, Inbred C57BL ; Middle Aged ; Spleen/microbiology ; Young Adult
    Print ISSN: 0036-8075
    Electronic ISSN: 1095-9203
    Topics: Biology , Chemistry and Pharmacology , Computer Science , Medicine , Natural Sciences in General , Physics
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  • 3
    Publication Date: 2015-04-25
    Description: Inflammatory CD4(+) T cell responses to self or commensal bacteria underlie the pathogenesis of autoimmunity and inflammatory bowel disease (IBD), respectively. Although selection of self-specific T cells in the thymus limits responses to mammalian tissue antigens, the mechanisms that control selection of commensal bacteria-specific T cells remain poorly understood. Here, we demonstrate that group 3 innate lymphoid cell (ILC3)-intrinsic expression of major histocompatibility complex class II (MHCII) is regulated similarly to thymic epithelial cells and that MHCII(+) ILC3s directly induce cell death of activated commensal bacteria-specific T cells. Further, MHCII on colonic ILC3s was reduced in pediatric IBD patients. Collectively, these results define a selection pathway for commensal bacteria-specific CD4(+) T cells in the intestine and suggest that this process is dysregulated in human IBD.〈br /〉〈br /〉〈a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4449822/" target="_blank"〉〈img src="https://static.pubmed.gov/portal/portal3rc.fcgi/4089621/img/3977009" border="0"〉〈/a〉   〈a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4449822/" target="_blank"〉This paper as free author manuscript - peer-reviewed and accepted for publication〈/a〉〈br /〉〈br /〉〈span class="detail_caption"〉Notes: 〈/span〉Hepworth, Matthew R -- Fung, Thomas C -- Masur, Samuel H -- Kelsen, Judith R -- McConnell, Fiona M -- Dubrot, Juan -- Withers, David R -- Hugues, Stephanie -- Farrar, Michael A -- Reith, Walter -- Eberl, Gerard -- Baldassano, Robert N -- Laufer, Terri M -- Elson, Charles O -- Sonnenberg, Gregory F -- DK071176/DK/NIDDK NIH HHS/ -- DP5 OD012116/OD/NIH HHS/ -- DP5OD012116/OD/NIH HHS/ -- UL1-RR024134/RR/NCRR NIH HHS/ -- Wellcome Trust/United Kingdom -- New York, N.Y. -- Science. 2015 May 29;348(6238):1031-5. doi: 10.1126/science.aaa4812. Epub 2015 Apr 23.〈br /〉〈span class="detail_caption"〉Author address: 〈/span〉Jill Roberts Institute for Research in Inflammatory Bowel Disease, Joan and Sanford I. Weill Department of Medicine, Gastroenterology Division, and Department of Microbiology and Immunology, Weill Cornell Medical College, Cornell University, New York, NY, USA. ; Jill Roberts Institute for Research in Inflammatory Bowel Disease, Joan and Sanford I. Weill Department of Medicine, Gastroenterology Division, and Department of Microbiology and Immunology, Weill Cornell Medical College, Cornell University, New York, NY, USA. Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA. ; Division of Gastroenterology, Hepatology, and Nutrition, Children's Hospital of Philadelphia, Philadelphia, PA, USA. ; Medical Research Council, Centre for Immune Regulation, College of Medical and Dental Sciences, University of Birmingham, Birmingham, UK. ; Department of Pathology and Immunology, University of Geneva Medical School, Geneva, Switzerland. ; Center for Immunology, Department of Laboratory Medicine and Pathology, University of Minnesota, MN, USA. ; Institut Pasteur, Microenvironment and Immunity Unit, Paris, France. ; Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA. Philadelphia Veterans Affairs Medical Center, Philadelphia, PA, USA. ; Departments of Medicine and Microbiology, University of Alabama at Birmingham, Birmingham, AL, USA. ; Jill Roberts Institute for Research in Inflammatory Bowel Disease, Joan and Sanford I. Weill Department of Medicine, Gastroenterology Division, and Department of Microbiology and Immunology, Weill Cornell Medical College, Cornell University, New York, NY, USA. gfsonnenberg@med.cornell.edu.〈br /〉〈span class="detail_caption"〉Record origin:〈/span〉 〈a href="http://www.ncbi.nlm.nih.gov/pubmed/25908663" target="_blank"〉PubMed〈/a〉
    Keywords: Animals ; Apoptosis/immunology ; Autoimmunity ; Bacteria/*immunology ; CD4-Positive T-Lymphocytes/*immunology ; Colon/*microbiology ; Female ; Flagellin/genetics/immunology ; Histocompatibility Antigens Class II/*immunology ; Humans ; *Immunity, Innate ; Inflammatory Bowel Diseases/immunology/*microbiology ; Lymphocyte Activation ; Male ; Mice ; Mice, Inbred C57BL ; Symbiosis ; Thymus Gland/immunology
    Print ISSN: 0036-8075
    Electronic ISSN: 1095-9203
    Topics: Biology , Chemistry and Pharmacology , Computer Science , Medicine , Natural Sciences in General , Physics
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Computational mechanics 21 (1998), S. 441-448 
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Many dynamic problems can be solved numerically by using Hamilton's law. The solution is expressed as a series in the time domain with undetermined coefficients. The unknown coefficients are determined by satisfying the Hamilton's law when the solution is allowed to have certain types of variations. The advantage of the method is that it can directly generate a set of algebraic equations without considering the dynamic equilibrium or the governing differential equations. In this paper, the essential features of the Hamilton's law and its variations are re-examined from the numerical perspectives. A general version of variation is proposed and the parametrized formulations are presented. The parametrized formulations unify conventional formulations and also yield many new ones. Illustrative numerical examples in this paper demonstrate that the conventional formulations may not be optimal although they may be rational.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Computational mechanics 17 (1996), S. 398-405 
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract  A new time finite-element method based on the extrapolation technique and the Galerkin time finite-element method is presented. In this method, the second-order governing differential equations of motion for dynamic problems are rewritten as a set of first order differential equations in state space. The standard Galerkin method is then employed for the temporal discretization. The algorithm is first-order accurate only. Based on the first-order Galerkin time finite-element formulation, the extrapolation technique is introduced to improve the order of accuracy. It is achieved by expressing the numerical amplification matrix of higher-order algorithm as a linear combination of the basic amplification matrices evaluated at selected instances of time. The matrices are combined with different weighting factors. The pairs of the selected instance of time and the corresponding weighting factors are free parameters. Unconditionally stable higher-order accurate formulations can be derived by properly choosing the free parameters. Algorithms up to fourth-order accurate are presented in this paper. Detailed analyses on stability, numerical dissipation and numerical dispersion are also given. Comparisons of the present algorithms with some well-known time-integration methods are presented to demonstrate the versatility of the present method, in particular its accuracy in the higher-order formulations.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In part I of this paper, we presented a consistent mathematical perspective to the formulations of Hamilton's law and unified the formulations by parametrized form with global approximation. In part II of this paper, we extend the formulations to a proper form to develop high-performance time finite elements for numerical solutions of dynamic problems. The two-field mixed formulations are emphasized and the particular features of using lower order interpolation functions are discussed.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Computational mechanics 17 (1996), S. 398-405 
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A new time finite-element method based on the extrapolation technique and the Galerkin time finite-element method is presented. In this method, the second-order governing differential equations of motion for dynamic problems are rewritten as a set of first order differential equations in state space. The standard Galerkin method is then employed for the temporal discretization. The algorithm is first-order accurate only. Based on the first-order Galerkin time finite-element formulation, the extrapolation technique is introduced to improve the order of accuracy. It is achieved by expressing the numerical amplification matrix of higher-order algorithm as a linear combination of the basic amplification matrices evaluated at selected instances of time. The matrices are combined with different weighting factors. The pairs of the selected instance of time and the corresponding weighting factors are free parameters. Unconditionally stable higher-order accurate formulations can be derived by properly choosing the free parameters. Algorithms up to fourth-order accurate are presented in this paper. Detailed analyses on stability, numerical dissipation and numerical dispersion are also given. Comparisons of the present algorithms with some well-known time-integration methods are presented to demonstrate the versatility of the present method, in particular its accuracy in the higher-order formulations.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 337-356 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic stiffness method is extended to large amplitude free and forced vibrations of frames. When the steady state vibration is concerned, the time variable is replaced by the frequency parameter in the Fourier series sense and the governing partial differential equations are replaced by a set of ordinary differential equations in the spatial variables alone. The frequency-dependent shape functons are generated approximately for the spatial discretization. These shape functions are the exact solutions of a beam element subjected to mono-frequency excitation and constant axial force to minimize the spatial discretization errors. The system of ordinary differential equations is replaced by a system of non-linear algebraic equations with the Fourier coefficients of the nodal displacements as unknowns. The Fourier nodal coefficients are solved by the Newtonian algorithm in an incremental manner. When an approximate solution is available, an improved solution is obtained by solving a system of linear equations with the Fourier nodal increments as unknowns. The method is very suitable for parametric studies. When the excitation frequency is taken as a parameter, the free vibration response of various resonances can be obtained without actually computing the linear natural modes. For regular points along the response curves, the accuracy of the gradient matrix (Jacobian or tangential stiffness matrix) is secondary (cf. the modified Newtonian method). However, at the critical positions such as the turning points at resonances and the branching points at bifurcations, the gradient matrix becomes important. The minimum number of harmonic terms required is governed by the conditions of completeness and balanceability for predicting physically realistic response curves. The evaluations of the newly introduced mixed geometric matrices and their derivatives are given explicitly for the computation of the gradient matrix.
    Additional Material: 7 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 4501-4527 
    ISSN: 0029-5981
    Keywords: time-step integration ; step-response matrix ; impulsive-response matrix ; structural dynamics ; recursive evaluation procedure ; non-proportional damping ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a precise time-step integration method for dynamic problems is presented. The second-order differential equations for dynamic problems are manipulated directly. A general damping matrix is considered. The transient responses are expressed in terms of the steady-state responses, the given initial conditions and the step-response and impulsive-response matrices. The steady-state responses for various types of excitations are readily obtainable. The computation of the step-response and impulsive-response matrices and their time derivatives are studied in this paper. A direct computation of these matrices using the Taylor series solutions is not efficient when the time-step size Δt is not small. In this paper, the recurrence formulae relating the response matrices at t=Δt to those at t=Δt/2 are constructed. A recursive procedure is proposed to evaluate these matrices at t=Δt from the matrices at t=Δt/2m. The matrices at t=Δt/2m are obtained from the Taylor series solutions. To improve the computational efficiency, the relations between the response matrices and their time derivatives are investigated. In addition, these matrices are expressed in terms of two symmetric matrices that can also be evaluated recursively. Besides, from the physical point of view, these matrices should be banded for small Δt. Both the stability and accuracy characteristics of the present algorithm are studied. Three numerical examples are used to illustrate the highly precise and stable algorithm. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 8 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3475-3495 
    ISSN: 0029-5981
    Keywords: structural dynamics ; time finite elements ; Hermitian shape functions ; unconditionally stable algorithms ; higher-order accurate algorithms ; time-step integration ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, single step time finite elements using the cubic Hermitian shape functions to interpolate the solution over a time interval are considered. The second-order differential equations are manipulated directly. Both the effects of modal damping and external excitation are considered. The accuracy of the solutions at the end of the time interval and the interpolated solutions within the time interval is investigated. The weighted residual approach is adopted to derive the time-integration algorithms. Instead of specifying the weighting functions, the weighting parameters are used to control the characteristics of the time finite elements. The weighting parameters are chosen to eliminate the higher-order truncation error terms or to enforce the asymptotic annihilation condition. A one-parameter family of third-order accurate asymptotically annihilating algorithms and another one-parameter family of fourth-order accurate non-dissipative algorithms are presented. The ranges of the weighting parameters for unconditionally stable algorithms are given. It is found that one of the members in each family corresponds to the Padé approximants of the exponential function in solving the first-order differential equations. Some of the existing unconditionally stable higher-order accurate algorithms are re-derived by the present unified approach.
    Additional Material: 7 Ill.
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