First- and second-order asymptotic solutions of fast fracture in an elastic–viscoplastic solid

International Journal of Non-Linear Mechanics ◽

10.1016/s0020-7462(00)00054-8 ◽

2001 ◽

Vol 36 (5) ◽

pp. 861-877 ◽

Author(s):

Meng Lu ◽

Qing-Hua Qin

Keyword(s):

Second Order ◽

Asymptotic Solutions ◽

Viscoplastic Solid ◽

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Uniform Asymptotic Solutions of a Class of Second-Order Linear Differential Equations Having a Turning Point and a Regular Singularity, with an Application to Legendre Functions

SIAM Journal on Mathematical Analysis ◽

10.1137/0517033 ◽

1986 ◽

Vol 17 (2) ◽

pp. 422-450 ◽

Author(s):

W. G. C. Boyd ◽

T. M. Dunster

Keyword(s):

Differential Equations ◽

Turning Point ◽

Second Order ◽

Linear Differential Equations ◽

Asymptotic Solutions ◽

Legendre Functions ◽

Regular Singularity ◽

Order Linear ◽

Linear Differential

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Asymptotic solutions of the second order for LE waves in corrugated rectangular waveguides

2016 IEEE International Conference on Mathematical Methods in Electromagnetic Theory (MMET) ◽

10.1109/mmet.2016.7544067 ◽

2016 ◽

Author(s):

Valentyn F. Borulko

Keyword(s):

Second Order ◽

Asymptotic Solutions ◽

Rectangular Waveguides

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Error bounds for asymptotic solutions of second-order linear difference equations

Journal of Computational and Applied Mathematics ◽

10.1016/0377-0427(95)00218-9 ◽

1996 ◽

Vol 71 (2) ◽

pp. 191-212 ◽

Author(s):

J.M. Zhang ◽

X.C. Li ◽

C.K. Qu

Keyword(s):

Difference Equations ◽

Error Bounds ◽

Second Order ◽

Asymptotic Solutions ◽

Linear Difference Equations ◽

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On fast fracture in an elastic-(plastic)-viscoplastic solid Part II – The motion of crack

International Journal of Fracture ◽

10.1023/b:frac.0000045720.76731.5e ◽

2004 ◽

Vol 129 (2) ◽

pp. 177-195 ◽

Author(s):

Meng Lu ◽

Yiu-Wing Mai

Keyword(s):

Elastic Plastic ◽

Viscoplastic Solid ◽

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Asymptotic solutions of an eigenvalue problem with several second-order turning points

IMA Journal of Applied Mathematics ◽

10.1093/imamat/48.1.39 ◽

1992 ◽

Vol 48 (1) ◽

pp. 39-51 ◽

Author(s):

ABDUL-MAJID WAZWAZ

Keyword(s):

Eigenvalue Problem ◽

Turning Points ◽

Second Order ◽

Asymptotic Solutions

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Connection Formulas for Asymptotic Solutions of Second Order Turning Points in Unbounded Domains

SIAM Journal on Mathematical Analysis ◽

10.1137/0504010 ◽

1973 ◽

Vol 4 (1) ◽

pp. 89-103 ◽

Author(s):

Anthony Wing-Kwok Leung

Keyword(s):

Turning Points ◽

Unbounded Domains ◽

Second Order ◽

Asymptotic Solutions ◽

Connection Formulas

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Asymptotic solutions of second‐order linear equations with three transition points

Journal of Mathematical Physics ◽

10.1063/1.1666582 ◽

1974 ◽

Vol 15 (12) ◽

pp. 2063-2066 ◽

Author(s):

Ali H. Nayfeh

Keyword(s):

Linear Equations ◽

Second Order ◽

Asymptotic Solutions ◽

Order Linear ◽

Transition Points

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The asymptotic solutions of ordinary linear differential equations of the second order, with special reference to a turning point

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-1949-0033420-2 ◽

1949 ◽

Vol 67 (2) ◽

pp. 461-461 ◽

Author(s):

Rudolph E. Langer

Keyword(s):

Differential Equations ◽

Special Reference ◽

Turning Point ◽

Second Order ◽

Linear Differential Equations ◽

Asymptotic Solutions ◽

Linear Differential ◽

Ordinary Linear Differential Equations

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Asymptotic Solutions and Radiation Conditions for Second-Order Diffracted Waves

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.3257148 ◽

1989 ◽

Vol 111 (3) ◽

pp. 203-207

Author(s):

H. Huang ◽

J. Li ◽

X. Wang

Keyword(s):

Finite Element ◽

Circular Cylinder ◽

Second Order ◽

Asymptotic Solutions ◽

Wave Forces ◽

Far Field ◽

Two Dimensional ◽

Diffracted Waves ◽

Artificial Boundaries ◽

Radiation Conditions

The far-field asymptotic solutions for the second-order diffracted waves have been developed, both in three and two-dimensional problems. The radiation conditions for the second-order diffracted waves are derived by using the asymptotic solutions. The nonlinear wave forces on a half-circular cylinder on seabed are presented by using finite element methods with the radiation conditions imposed on the artificial boundaries.

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Error Bounds for Asymptotic Solutions of Second-Order Differential Equations Having an Irregular Singularity of Arbitrary Rank

Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis ◽

10.1137/0702018 ◽

1965 ◽

Vol 2 (2) ◽

pp. 244-249 ◽

Author(s):

F. W. J. Olver ◽

F. Stenger

Keyword(s):

Differential Equations ◽

Error Bounds ◽

Second Order ◽

Asymptotic Solutions ◽

Irregular Singularity ◽

Second Order Differential Equations ◽

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