baram2584/MultiPhysicsVault
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

add documents
Tests / Hermetic test suite (push) Has been cancelled
Details
Tests / Skill frontmatter validation (push) Has been cancelled
Details

Browse Source
This commit is contained in:
김경종
2026-05-29 15:59:56 +09:00
parent 4cc312954f
commit b7f84e1c0f
14412 changed files with 231953 additions and 0 deletions
Download Patch File Download Diff File Expand all files Collapse all files
.raw/AbaqusTheoriesManual/AbaqusTheoriesManual_084.md
+225
View File
@@ -0,0 +1,225 @@
<!-- source-page: 831 -->
# References
Methods for Transient Analysis ), Ed. T. Belytschko and T. R. J. Hughes, Elsevier, 1983.
Cormeau, I., \`\`Numerical Stability in Quasi-Static Elasto-Visco Plasticity ,'' International Journal for Numerical Methods in Engineering, vol. 9, pp. 109-127, 1975.
Cotterell, B., and J. R. Rice, \`\`Slightly Curved or Kinked Cracks,'' International Journal of Fracture, vol. 16, pp. 155-169, 1980.
Cowper, G. R., \`\`Gaussian Quadrature for Triangles,'' International Journal for Numerical Methods in Engineering, vol. 7, pp. 405-408, 1973.
Crank, J., The Mathematics of Diffusion, Clarendon Press, Oxford, 1956.
Crisfield, M. A., \`\`A Fast Incremental/Iteration Solution Procedure that Handles \`Snap-Through' ,'' Computers and Structures, vol. 13, pp. 55-62, 1981.
Crisfield, M. A., \`\`Snap-Through and Snap-Back Response in Concrete Structures and the Dangers of Under-Integration,'' International Journal for Numerical Methods in Engineering, vol. 22, pp. 751-767, 1986.
DeGroot, S. R., and P. Mazur, Non Equilibrium Thermodynamics, North Holland Publishing Company, North Holland, Amsterdam, 1962.
DeRuntz, J. A., Jr., T. L. Geers, and C. A. Felippa, The Underwater Shock Analysis (USA-Version 3) Code, A Reference Manual, DNA 5615F, Defense Nuclear Agency, Washington, D. C., 1980.
DeRuntz, J. A., Jr., "The Underwater Shock Analysis Code and its Applications, " 60th Shock and Vibration Symposium Proceedings, vol. 1, pp. 89-107, David Taylor Research Center, Bethesda, Maryland, November 1989.
Desai, C. S., "Finite Element Methods for Flow in Porous Media, " in Finite Elements in Fluids, vol. 1, Wiley, London, pp. 157-181, 1975.
Dodge, W. G., and S. E. Moore, \`\`Stress Indices and Flexibility Factors for Moment Loadings on Elbows and Curved Pipes,'' Welding Research Council Bulletin, no. 179, December 1972.
Drucker, D. C., and W. Prager, \`\`Soil Mechanics and Plastic Analysis or Limit Design,'' Quarterly of Applied Mathematics, vol. 10, pp. 157-165, 1952.
Du, Z. -Z., and J. W. Hancock, \`\`The Effect of Non-Singular Stresses on Crack-Tip Constraint,'' Journal of the Mechanics and Physics of Solids, vol. 39, pp. 555-567, 1991.
Dupuis, G., \`\`Stabilité Elastique des Structures Unidimensionelles ,'' ZAMP, vol. 20, pp. 94-106, 1969.
Eleiche, A. S. M., \`\`A Literature Survey of the Combined Effects of Strain Rate and Elevated Temperature on the Mechanical Properties of Metals,'' Air Force Materials Laboratories, Report AFML-TR-72-125, 1972.
Ericsson, T., and A. Ruhe, \`\`The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems,'' Mathematics of Computation, vol. 35, pp. 1251-1268, 1980.
Erdogan, F., and G. C. Sih, \`\`On the Crack Extension in Plates under Plane Loading and Transverse
<!-- source-page: 832 -->
# References
Shear,'' Journal of Basic Engineering, vol. 85, pp. 519-527, 1963.
Faltinsen, O. M., Sea Loads on Ships and Offshore Structures , Cambridge University Press, 1990.
Farin, G., Curves and Surfaces for Computer Aided Geometric Design , Academic Press, San Diego, Second Edition, 1990.
Farin, G., "Smooth Interpolation to Scattered 3D Data," in Surfaces in Computer Aided Geometric Design, Barnhill, R. E. and Boehm, W., eds., North-Holland, pp. 43-63, 1983.
Flanagan, D. P., and T. Belytschko, \`\`A Uniform Strain Hexahedron and Quadrilateral with Orthogonal Hourglass Control,'' International Journal for Numerical Methods in Engineering , vol. 17, pp. 679-706, 1981.
Flugge, W., Tensor Analysis and Continuum Mechanics , Springer-Verlag, New York, 1972.
Gao, H., M. Abbudi, and D. M. Barnett, \`\`Interfacial Crack-Tip Fields in Anisotropic Elastic Solids ,'' Journal of the Mechanics and Physics of Solids, vol. 40, pp. 393-416, 1992.
Geers, T. L., \`\`Doubly Asymptotic Approximations for Transient Motions of Submerged Structures,'' Journal of the Acoustical Society of America, vol. 64, no. 5, pp. 1500-1508, 1978.
Gibson, L. J., and M. F. Ashby, \`\`The Mechanics of Three-Dimensional Cellular Materials,'' Proceedings of the Royal Society, London, A 382, pp. 43-59, 1982.
Gibson, L. J., M. F. Ashby, G. S. Schajer, and C. I. Robertson, \`\`The Mechanics of Two-Dimensional Cellular Materials,'' Proceedings of the Royal Society, London, A 382, pp. 25-42, 1982.
Green, A. E., and P. M. Naghdi, \`\`A General Theory of an Elastic-Plastic Continuum,'' Archives of Rational Mechanics and Analysis, vol. 17.
Grimes, R. G., J. G. Lewis, and H. D. Simon, \`\`A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems,'' SIAM Journal on Matrix Analysis and Applications, vol. 15, pp. 228-272, 1994.
Grote, M., and J. Keller, \`\`On Nonreflecting Boundary Conditions,'' Journal of Computational Physics, vol. 122, pp. 231-243, 1995.
Gudehus, G., Editor, Finite Elements in Geomechanics, Wiley and Sons, 1977.
Gupta, A. K., Response Spectrum Method in Seismic Analysis and Design of Structures , Blackwell Scientific Publications, 1990.
Gurson, A. L., \`\`Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I--Yield Criteria and Flow Rules for Porous Ductile Materials ,'' Journal of Engineering Materials and Technology, vol. 99, pp. 2-15, 1977.
Hansen, H. T., Nonlinear Static and Dynamic Analysis of Slender Structures Subjected to Hydrodynamic Loading, University of Trondheim, Norway, 1988.
Hayashi, K., and S. Nemat-Nasser, \`\`Energy-Release Rate and Crack Kinking under Combined Loading,'' Journal of Applied Mechanics, vol. 48, pp. 520-524, 1981.
<!-- source-page: 833 -->
# References
He, M. -Y., and J. W. Hutchinson, "Kinking of a Crack out of an Interface: Tabulated Solution Coefficients," Harvard University, Cambridge, Massachusetts, Division of Applied Mechanics, 1989.
Hegemier, G. A., "Evaluation of Models for MX Siting, Volume II--Reinforced Concrete Models," Systems, Science and Software, Report SSS-R-80-4155, La Jolla, California, 1979.
Hegemier, G. A., "Evaluation of Models for MX Siting, Volume II--Reinforced Concrete Models," Systems, Science and Software, Report SSS-R-80-4155, La Jolla, California, 1979.
Hegemier, G. A., and K. J. Cheverton, "Evaluation of Reinforced Concrete Models for Nuclear Power Plant Application," EPRI, Palo Alto, California, 1980.
Hibbitt, H. D., \`\`Some Follower Forces and Load Stiffness,'' International Journal for Numerical Methods in Engineering, vol. 14, pp. 937-941, 1979.1979.
Hibbitt, H. D., "Special Structural Elements of Piping Analysis," Pressure Vessels and Piping; Analysis and Computers, ASME, New York, 1974.
Hibbitt, H. D., and B. I. Karlsson, "Analysis of Pipe Whip," EPRI, Report NP-1208, 1979.
Hilber, H. M., T. J. R. Hughes, and R. L. Taylor, \`\`Collocation, Dissipation and \`Overshoot' for Time Integration Schemes in Structural Dynamics,'' Earthquake Engineering and Structural Dynamics, vol. 6, pp. 99-117, 1978.
Hilderbrand, F. B., Introduction to Numerical Analysis , McGraw Hill, 1974.
Hilleborg, A., M. Modeer, and P. E. Petersson, \`\`Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements,'' Cement and Concrete Research, vol. 6, pp. 773-782, 1976.
Hjelm, H. E., "Elastoplasticity of Grey Cast Iron, FE-Algorithms and Biaxial Experiments," Ph.D. Thesis, Chalmers University of Technology, Division of Solid Mechanics, Sweden, 1992.
Hjelm, H. E., \`\`Yield Surface for Grey Cast Iron under Biaxial Stress,'' Journal of Engineeringfor Materials and Technology, vol. 116, pp. 148-154, 1994.
Hoenig, A., \`\`Near-Tip Behavior of a Crack in a Plane Anisotropic Elastic Body,'' Engineering Fracture Mechanics, vol. 16, pp. 393-403, 1982.
Holman, J. P., Heat Transfer, McGraw-Hill, 1990.
Hughes, T. J. R., and A. Brooks, "A Theoretical Framework for Petrov-Galerkin Methods with Discontinuous Weighting Functions," in Finite Elements in Fluids, vol. 4, edited by R. H. Gallagher, D. H. Norrie, J. T. Oden, and O. C. Zienkiewicz, John Wiley & Sons, 1982.
Hughes, T. J. R., and W. K. Liu, "Nonlinear Finite Element Analysis of Shells, Part I: Three-Dimensional Shells," California Institute of Technology, Pasadena, California, 1980.
Hughes, T. J. R., R. L. Taylor, and W. Kanoknukulchai, \`\`A Simple and Efficient Element for Plate Bending,'' International Journal for Numerical Methods in Engineering, vol. 11, no. 10, pp. 1529-1543, 1977.
<!-- source-page: 834 -->
# References
Hughes, T. J. R., and T. E. Tezduyar, \`\`Finite Elements based upon Mindlin Plate Theory with Particular Reference to the Four-Node Bilinear Isoparametric Element,'' Journal of Applied Mechanics, pp. 587-596, 1981.
Hughes, T. J. R., and J. Winget, \`\`Finite Rotation Effects in Numerical Integration of Rate Constitutive Equations Arising in Large Deformation Analysis,'' International Journal for Numerical Methods in Engineering, vol. 15, pp. 1862-1867, 1980.
Hurty, W. C., and M. F. Rubinstein, Dynamics of Structures, Prentice-Hall, Englewood Cliffs, New Jersey, 1964.
Hussain, M. A., S. L. Pu, and J. Underwood, \`\`Strain-Energy-Release Rate for a Crack under Combined Mode I and Mode II,'' ASTM-STP-560, pp. 2-28, 1974.
Hutchinson, J. W., \`\`Singular Behaviour at the End of a Tensile Crack in a Hardening Material ,'' Journal of the Mechanics and Physics of Solids, vol. 16, pp. 13-31, 1968.
Hutchinson, J. W., and Z. Suo, \`\`Mixed Mode Cracking in Layered Materials,'' Advances in Applied Mechanics, vol. 29, pp. 63-191, 1992.
Irons, B., and S. Ahmad, Techniques of Finite Elements, Ellis Horwood Limited, Halsted Press, John Wiley and Sons, Chichester, England, 1980.
Johnson, D., "Surface to Surface Radiation in the Program TAU, Taking Account of Multiple Reflection," United Kingdom Atomic Energy Authority Report ND-R-1444(R), 1987.
Kaliske, M., and H. Rothert, \`\`On the Finite Element Implementation of Rubber-like Materials at Finite Strains,'' Engineering Computations, vol. 14, no. 2, pp. 216-232, 1997.
Kawabata, S., Y. Yamashita, H. Ooyama, and S. Yoshida, \`\`Mechanism of Carbon-Black Reinforcement of Rubber Vulcanizate,'' Rubber Chemistry and Technology, vol. 68, no. 2, pp. 311-329, 1995.
Der Kiureghian, A., \`\`A Response Spectrum Method For Random Vibration Analysis of MDF Systems,'' Earthquake Engineering and Structural Dynamics, vol. 9, pp. 419-435, 1981.
Kennedy, J. M., T. Belytschko, and J. I. Lin, \`\`Recent Developments in Explicit Finite Element Techniques and Their Applications to Reactor Structures ,'' Nuclear Engineering and Design, vol. 96, pp. 1-24, 1986.
Kfouri, A. P., \`\`Some Evaluations of the Elastic T-Term Using Eshelby's Method,'' International Journal of Fracture, vol. 30, pp. 301-315, 1986.
Kilian, H.-G., \`\`Equation of State of Real Networks,'' Polymer, vol. 22, pp. 209-216, 1981.
Kilian, H.-G., H. F. Enderle, and K. Unseld, \`\`The Use of the van der Waals Model to Elucidate Universal Aspects of Structure-Property Relationships in Simply Extended Dry and Swollen Rubbers,'' Colloid and Polymer Science, vol. 264, pp. 866-876, 1986.
Kleiber, M., H. Antúnez, T. D. Hien, and P. Kowalczyk, Parameter Sensitivity in Nonlinear Mechanics, John Wiley & Sons, 1997.
<!-- source-page: 835 -->
# References
Kumar, V., M. D. German, and C. F. Shih, "An Engineering Approach for Elastic-Plastic Fracture Analysis," Electric Power Research Institute Report NP-1931, Project 1237-1, Electric Power Research Institute, Palo Alto, CA, 1981.
Kwata, K., S. Asai, and H. Takeda, "A Solution for the IAEA International Piping Benchmark Problem," Century Research Corporation, Tokyo, 1978.
Lamb, H., Hydrodynamics, Dover Publications, New York, 1945.
Larsson, S. G., and A. J. Carlsson, \`\`Influence of Non-Singular Stress Terms and Specimen Geometry on Small-Scale Yielding at Crack Tips in Elastic-Plastic Material ,'' Journal of the Mechanics and Physics of Solids, vol. 21, pp. 263-278, 1973.
Lemaitre, J., and J.-L. Chaboche, Mechanics of Solid Materials, Cambridge University Press, 1990.
Lianis, G., "Small Deformations Superposed on an Initial Large Deformation in Viscoelastic Bodies, " Proceedings of the 4th International Congress on Rheology, part 2, pp. 109-119, Interscience, New York, 1965.
Lin, C. S., and A. C. Scordelis, \`\`Nonlinear Analysis of RC Shells of General Form,'' ASCE, Journal of Structural Engineering, vol. 101, pp. 523-538, 1975.
Lindholm, J. S., and R. L. Besseny, \`\`A Survey of Rate Dependent Strength Properties of Metals,'' Air Force Materials Laboratory, Report AFML-TR-69-119, 1969.
Lysmer, J., and R. L. Kuhlemeyer, \`\`Finite Dynamic Model for Infinite Media,'' Journal of the Engineering Mechanics Division of the ASCE, pp. 859-877, August 1969.
MacNeal, R. H., \`\`A Simple Quadrilateral Shell Element,'' Computers and Structures, vol. 8, pp. 175-183, 1978.
MacNeal, R. H., \`\`Derivation of Element Stiffness Matrices by Assumed Strain Distributions ,'' Nuclear Engineering and Design, vol. 70, pp. 3-12, 1982.
Maiti, S. K., L. J. Gibson, and M. F. Ashby, \`\`Deformation and Energy Absorption Diagrams for Cellular Solids,'' Acta Metallurgica, vol. 32, no. 11, pp. 1963-1975, 1984.
Maiti, S. K., and R. A. Smith, \`\`Comparison of the Criteria for Mixed Mode Brittle Fracture Based on the Preinstability Stress-Strain Field, Part I: Slit and Elliptical Cracks under Uniaxial Tensile Loading,'' International Journal of Fracture, vol. 23, pp. 281-295, 1983.
Mang, H. A., \`\`Symmetricability of Pressure Stiffness Matrices for Shells with Loaded Free Edges,'' International Journal for Numerical Methods in Engineering, vol. 15, pp. 981-990, 1980.
Matthies, H., and G. Strang, \`\`The Solution of Nonlinear Finite Element Equations ,'' International Journal for Numerical Methods in Engineering, vol. 14, pp. 1613-1626, 1979.
Menétrey, Ph., and K. J. William, "Triaxial Failure Criterion for Concrete and its Generalization, " ACI Structural Journal, 92:311-18, May/June, 1995.
Morman, K. N., "Analytical Prediction of Elastomeric Mount Dynamic Characteristics," Report L2143-2, Ford Engineering Computer Systems, Car Engineering, Dearborn, Michigan, 1979.
<!-- source-page: 836 -->
# References
Morman, K. N., and J. C. Nagtegaal, \`\`Finite Element Analysis of Sinusoidal Small-Amplitude Vibrations in Deformed Viscoelastic Solids. Part I: Theoretical Development ,'' International Journal of Numerical Methods in Engineering, vol. 19, pp. 1079-1103, 1983.
Morse, P., and K. Ingard, Theoretical Acoustics, McGraw-Hill, 1968.
Murff, J. D., Private communication, 1982.
Nagtegaal, J. C., D. M. Parks, and J. R. Rice, \`\`On Numerically Accurate Finite Element Solutions in the Fully Plastic Range,'' Computer Methods in Applied Mechanics and Engineering, vol. 4, pp. 153-177, 1977.
Nakamura, T., and D. M. Parks, \`\`Antisymmetrical 3-D Stress Field near the Crack Front of a Thin Elastic Plate,'' International Journal of Solids and Structures , vol. 25, pp. 1411-1426, 1989.
Nakamura, T., and D. M. Parks, \`\`Determination of Elastic T-Stress along Three-dimensional Crack Fronts Using an Interaction Integral,'' International Journal of Solids and Structures , vol. 28, pp. 1597-1611, 1992.
Nayak, G. C., and O. C. Zienkiewicz, \`\`A Convenient Form of Invariants and its Application to Plasticity,'' Proceedings of the ASCE, Engineering Mechanics Division, vol. 98, no. St4, pp. 949-954, 1972.
Needleman, A., and V. Tvergaard, \`\`Necking of Biaxially Stretched Elastic-Plastic Circular Plates,'' Journal of the Mechanics and Physics of Solids, vol. 25, pp. 159-183, 1977.
Newman, M., and A. Pipano, \`\`Fast Modal Extraction in NASTRAN via the FEER Computer Program,'' NASA TM X-2893, pp. 485-506, 1973.
Newmark, N. M., J. A. Blume, and K. K. Kapur, \`\`Seismic Design Spectra for Nuclear Power Plants,'' Power Division Journal, ASCE, 99, P02, Proceedings Paper 10142 , pp. 287-303, 1973.
Nguyen, H. V., and D. F. Durso, \`\`Absorption of Water by Fiber Webs: an Illustration of Diffusion Transport,'' Tappi Journal, vol. 66, no. 12, 1983.
Nishimura, H., M. Isobe, and K. Horikawa, \`\`Higher Order Solutions of Stokes and Cnoidal Waves ,'' Journal of Faculty Engineering, University of Tokyo (B), vol. 34, no. 2, 1977.
Nuclear Standard NE F 9-5T, "Guidelines and Procedures for Design of Class 1 Elevated Temperature Nuclear System Components," United States Department of Energy, Nuclear Energy Programs, March 1981.
Oden, J. T., Mechanics of Elastic Structures , McGraw-Hill, New York, 1967.
Oden, J. T., and N. Kikuchi, "Finite Element Methods for Constrained Problems in Elasticity, " TICOM, University of Texas at Austin, Austin, Texas, 1980.
Oden, J. T., and N. Kikuchi, "Finite Element Methods for Constrained Problems in Elasticity, " Fifth Invitational Symposium on the Unification of Finite Elements--Finite Differences and Calculus of Variations, Edited by H. Kardestuncer, University of Connecticut, Storrs, CT.
Oden, J. T., and E. B. Pires, \`\`Nonlocal and Nonlinear Friction Laws and Variational Principles for
<!-- source-page: 837 -->
# References
Contact Problems in Elasticity,'' Journal of Applied Mechanics, vol. 50, pp. 67-73, 1983.
Ohtsubo, H., and O. Watanabe, \`\`Flexibility and Stress Factors for Pipe Bends--An Analysis by the Finite Ring Method,'' ASME paper 76-PVP-40, 1976.
Palaniswamy, K., and W. G. Knauss, "On the Problem of Crack Extension in Brittle Solids under General Loading," Mechanics Today, Edited by S. Nemat-Nasser, Vol. 4, Pergamon Press, 1978.
Papoulis, A., Probability, Random Variables, and Stochastic Processes , McGraw-Hill, New York, 1965.
Parks, D. M., \`\`The Virtual Crack Extension Method for Nonlinear Material Behavior ,'' Computer Methods in Applied Mechanics and Engineering, vol. 12, pp. 353-364, 1977.
Parks, D. M., "Advances in Characterization of Elastic-Plastic Crack-Tip Fields, " Topics in Fracture and Fatigue, Edited by A. S. Argon, Springer Verlag, 1992.
Parks, D. M., and C. S. White, \`\`Elastic-Plastic Line Spring Finite Elements for Surface Cracked Plates and Shells,'' Journal of Pressure Vessel Technology, vol. 104, pp. 287-292, 1982.
Park, K. C., C. A. Felippa, and J. A. DeRuntz, "Stabilization of Staggered Solution Procedures for Fluid-Structure Interaction Analysis," Computational Methods for Fluid-Structure Interaction Problems, Ed. T. Belytschko and T. L. Geers, AMD-Vol. 26, ASME, 1977.
Parlett, B. N., The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, New Jersey, 1980.
Parlett, B. N., and B. Nour-Omid, \`\`Toward a Black Box Lanczos Program,'' Computer Physics Communications, vol. 53, pp. 169-179, 1989.
Parry, R. H. G., Editor, Stress-Strain Behaviour of Soils , G. T. Foulis and Co., Henley, England, 1972.
Penzien, J., and M. Watabe, \`\`Characteristic of 3-Dimensional Earthquake Ground Motions ,'' Earthquake Engineering and Structural Dynamics, vol. 3, pp. 365-373, 1975.
Powell, G., and J. Simons, \`\`Improved Iterative Strategy for Nonlinear Structures,'' International Journal for Numerical Methods in Engineering, vol. 17, pp. 1455-1467, 1981.
Ramaswami, S., "Towards Optimal Solution Techniques for Large Eigenproblems in Structural Mechanics," Ph.D. Thesis, MIT, 1979.
Ramm, E., "Strategies for Tracing the Nonlinear Response Near Limit Points," Nonlinear Finite Element Analysis in Structural Mechanics , Edited by E. Wunderlich, E. Stein, and K.J. Bathe,Structural Mechanics Springer-Verlag, Berlin, 1981.
Rice, J. R., "The Line Spring Model for Surface Flaws," The Surface Crack: Physical Problems and Computational Solutions, J. L. Sedlow, Editor, ASME, 1972.
Rice, J. R., "Continuum Mechanics and Thermodynamics of Plasticity in Relation to Microscale Deformation Mechanisms," Constitutive Equations in Plasticity , Argon, A. S., Editor, MIT Press, Cambridge, Massachusetts, 1975.
Rice, J. R., and G. F. Rosengren, \`\`Plane Strain Deformation Near a Crack Tip in a Power Law
<!-- source-page: 838 -->
# References
Hardening Material,'' Journal of the Mechanics and Physics of Solids, vol. 16, pp. 1-12, 1968.
Rodal, J. J. A., and E. A. Witmer, \`\`Finite-Strain Large-Deflection Elastic-Viscoplastic Finite-Element Transient Response Analysis of Structures,'' NASA contractor, Report 159874, NASA Lewis, 1979.
Rots, J. G., and J. Blaauwendraad, \`\`Crack Models for Concrete: Discrete or Smeared? Fixed, Multi-directional or Rotating? ,'' HERON, vol. 34, no. 1, pp. 1-59, 1989.
Scheller, J. D., and R. Mallet, \`\`Numerical Evaluation of an Inelastic Piping Elbow Element,'' ASME Paper 79-PVP-41, 1979.
Schofield, A., and C. P. Wroth, Critical State Soil Mechanics , McGraw-Hill, New York, 1968.
Schreyer, H. L., R. F. Kulak, and J. M. Kramer, \`\`Accurate Numerical Solutions for Elastic-Plastic Models,'' Transactions of the ASME, Journal of Pressure Vessel Technology, vol. 101, no. 3, 1979.
Shih, C. F., and R. J. Asaro, \`\`Elastic-Plastic Analysis of Cracks on Bimaterial Interfaces: Part I--Small Scale Yielding,'' Journal of Applied Mechanics, pp. 299-316, 1988.
Shih, C. F., B. Moran, and T. Nakamura, \`\`Energy Release Rate along a Three-Dimensional Crack Front in a Thermally Stressed Body,'' International Journal of Fracture, vol. 30, pp. 79-102, 1986.
Siegel, R., and J. R. Howell, Thermal Radiation Heat Transfer, McGraw Hill, New York, 1980.
Sih, G. C., \`\`Some Basic Problems in Fracture Mechanics and New Concepts,'' Engineering Fracture Mechanics, vol. 5, pp. 365-377, 1973.
Sih, G. C., P. C. Paris, and G. R. Irwin, \`\`On Cracks in Rectilinearly Anisotropic Bodies ,'' International Journal of Fracture Mechanics, vol. 1, pp. 189-202, 1965.
Simo, J. C., \`\`On a Fully Three-Dimensional Finite-Strain Viscoelastic Damage Model: Formulation and Computational Aspects,'' Computer Methods in Applied Mechanics and Engineering, vol. 60, pp. 153-173, 1987.
Simo, J. C., \`\`(Symmetric) Hessian for Geometrically Nonlinear Models in Solid Mechanics: Intrinsic Definition and Geometric Interpretation,'' Computer Methods in Applied Mechanics and Engineering, vol. 96, no. 2, pp. 189-200, 1992.
Simo, J. C., and F. Armero, \`\`Geometrically Nonlinear Enhanced Strain Mixed Methods and the Method of Incompatible Modes,'' International Journal for Numerical Methods in Engineering, vol. 33, pp. 1413-1449, 1992.
Simo, J. C., D. D. Fox, and M. S. Rifai, \`\`On a Stress Resultant Geometrically Exact Shell Model. Part III: Computational Aspects of the Nonlinear Theory,'' Computer Methods in Applied Mechanics and Engineering, vol. 79, pp. 21-70, 1989.
Simo, J. C., and M. S. Rifai, \`\`A Class of Assumed Strain Methods and the Method of Incompatible Modes,'' International Journal for Numerical Methods in Engineering, vol. 29, pp. 1595-1638, 1990.
Simon, H. D., \`\`The Lanczos Algorithm with Partial Reorthogonalization,'' Mathematics of
<!-- source-page: 839 -->
# References
Computation, vol. 42, pp. 115-142, 1984.
Skjelbreia, L., and J. Hendrickson, "Fifth Order Gravity Wave Theory," Proceedings of the 87th Coastal England Conference, Chapter Ten, den Haag, 1960.
Smeby, W., and A. Der Kiureghian, \`\`Modal Combination Rules for Multicomponent Earthquake Excitation,'' Earthquake Engineering and Structural Dynamics, vol. 12, pp. 1-12, 1984.
Sobel, L. H., \`\`In-Plane Bending of Elbows,'' Computers and Structures, vol. 7, pp. 701-715, 1977.
Sofronis, P., and R. M. McMeeking, \`\`Numerical Analysis of Hydrogen Transport Near a BluntingHydrogen Transport Crack Tip,'' Journal of the Mechanics and Physics of Solids, vol. 37, no. 3, pp. 317-350, 1989.
Spence, J., "An Upper Bound Analysis for the Deformation of Smooth Pipe Bends in Creep," Second IUTAM Symposium on Creep in Structures, Goteberg, 1970, Springer Verlag, 1972.
Spring, K. W., \`\`Euler Parameters and the Use of Quaternion Algebra in the Manipulation of Finite Rotations: a Review,'' Mechanisms and Machine Theory, vol. 21, pp. 365-373, 1986.
Storåkers, B., \`\`On Material Representation and Constitutive Branching in Finite Compressible Elasticity,'' Journal of the Mechanics and Physics of Solids , vol. 34, no. 2, pp. 125-145, 1986.
Strang, G., Linear Algebra and Its Applications , Academic Press, New York, 1976.
Strang, G., and G. Fix, An Analysis of the Finite Element Method, Prentice-Hall, New York, 1973.
Stroh, A. N., \`\`Dislocation and Cracks in Anisotropic Elasticity ,'' Philosophical Magazine, vol. 7, pp.7, 625-646, 1958.
Stroud, A. H., Approximate Calculation of Multiple Integrals , Prentice-Hall, 1971.
Suo, Z., \`\`Singularities, Interfaces and Cracks in Dissimilar Anisotropic Media ,'' Proceedings of the Royal Society, London, A, vol. 427, pp. 331-358, 1990.
Symonds, P. S., "Survey of Methods of Analysis for Plastic Deformation of Structures under Dynamic Loading," Brown University, Division of Engineering Report, June 1967.
Symonds, P. S., T. C. T. Ting, and D. N. Robinson, "Survey of Progress in Plastic Wave Propagation in Solid Bodies," Brown University, Division of Engineering Report, June 1967.
Tada, H., C. Paris, and G. R. Irwin, The Stress Analysis of Cracks Handbook , Del Research Corporation, Hellertown, Pennsylvania, 1973.
Takeda, H., S. Asai, and K. Kwata, "A New Finite Element for Structural Analysis of Piping Systems," Proceedings of the Fifth SMIRT Conference, Berlin, 1979.
Tanaka, T., and D. J. Fillmore, \`\`Kinetics of Swelling of Gels,'' Journal of Chemical Physics, vol. 70,D. pp. 1214-1218, 1979.
Tariq, S. M., \`\`Evaluation of Flow Characteristics of Perforations Including Nonlinear Effects With the Finite Element Method,'' SPE Production Engineering, pp. 104-112, May 1987.
Taylor, R. L., P. J. Beresford, and E. L. Wilson, \`\`A Nonconforming Element for Stress Analysis,'' International Journal for Numerical Methods in Engineering, vol. 10, pp. 1211-1219, 1976.
<!-- source-page: 840 -->
# References
Theocaris, P. S., \`\`A Higher Order Approximation for the T-Criterion of Fracture in Biaxial Fields ,'' Engineering Fracture Mechanics, vol. 19, pp. 975-991, 1984.
Thompson, C. J., Classical Equilibrium Statistical Mechanics , Oxford University Press, New York, 1988.
Timoshenko, S. P., Strength of Materials; Part III, Advanced Theory and Problems , D. Van Nostrand Co., Princeton, New Jersey, Third Edition, 1956.
Treloar, L. R. G., The Physics of Rubber Elasticity, Clarendon Press, Oxford, Third Edition, 1975.
Tvergaard, V., \`\`Influence of Voids on Shear Band Instabilities under Plane Strain Condition ,'' International Journal of Fracture Mechanics, vol. 17, pp. 389-407, 1981.
Twizell, E. H., and R. W. Ogden, \`\`Non-linear Optimization of the Material Constants in Ogden's Stress-Deformation Function for Incompressible Isotropic Elastomers,'' Journal of the Australian Mathematical Society, Series B 24, pp. 424-434, 1986.
Wang, Y. -Y., \`\`A Two-Parameter Characterization of Elastic-Plastic Crack Tip Fields and Application to Cleavage Fracture,'' Ph.D. Thesis, Department of Mechanical Engineering, MIT, Cambridge, MA, 1991.
Weber, G., and L. Anand, \`\`Finite Deformation Constitutive Equations and a Time Integration Procedure for Isotropic, Hyperelastic-Viscoplastic Solids,'' Computer Methods in Applied Mechanics and Engineering, vol. 79, pp. 173-202, 1990.
Whitham, G. B., Linear and Nonlinear Waves, John Wiley & Sons, 1974.
Wilkinson, J. H., The Algebraic Eigenvalue Problem, Oxford University Press, Oxford, 1965.
Williams, M. L., \`\`On the Stress Distribution at the Base of a Stationary Crack ,'' Journal of Applied Mechanics, vol. 24, pp. 109-114, 1957.
Wilson, E. L., A. Der Kiureghian, and E. P. Bayo, \`\`A Replacement for the SRSS Method in Seismic Analysis,'' Earthquake Engineering and Structural Dynamics, vol. 9, pp. 187-192, 1981.
Wilson, E. L., R. L. Taylor, W. P. Doherty, and J. Ghaboussi, "Incompatible Displacement Models," in Numerical and Computer Models in Structural Mechanics , Eds. S. F. Fenves, N. Perrone, A. R. Robinson, and W. C. Schnobrich, Academic Press, New York, 1973.
Wu, T. H., Soil Mechanics, Allyn and Bacon, Boston, 1976.
Xu, G., F. Bower, and M. Ortiz, \`\`An Analysis of Non-Planar Crack Growth under Mixed Mode Loading,'' International Journal of Solids and Structures , vol. 31, pp. 2167-2193, 1994.
Yeoh, O. H., \`\`Some Forms of the Strain Energy Function for Rubber,'' Rubber Chemistry and Technology, vol. 66, pp. 754-771, 1993.
Yu, C. C., and J. C. Heinrich, \`\`Petrov-Galerkin Methods for the Time-Dependent Convective Transport Equation,'' International Journal for Numerical Methods in Engineering, vol. 23, pp. 883-902, 1986.
Yu, C. C., and J. C. Heinrich, \`\`Petrov-Galerkin Method for Multidimensional, Time-Dependent,