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Journal Articles

A Fixed-Point Iteration Method With Quadratic Convergence

K. P. Walker, T.-L. Sham
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research Papers
J. Appl. Mech. May 2012, 79(3): 031001.
https://doi.org/10.1115/1.4005878
Published Online: April 5, 2012
View Article titled, A Fixed-Point Iteration Method With Quadratic Convergence
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Topics: Algorithms, Approximation, Nonlinear equations, Differential equations, Boundary layers, Newton's method, Steady state
Journal Articles

Nonlinear Transient Response of Thermally Loaded Laminated Panels

D. C. D. Oguamanam, Mem. ASME, Assistant Professor,, J. S. Hansen, Professor,, G. R. Heppler, Professor,
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Technical Papers
J. Appl. Mech. January 2004, 71(1): 49–56.
https://doi.org/10.1115/1.1631033
Published Online: March 17, 2004
View Article titled, Nonlinear Transient Response of Thermally Loaded Laminated Panels
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Topics: Deformation, Inertia (Mechanics), Rotation, Newton's method, Transients (Dynamics), Displacement, Heat flux
Journal Articles

Response Power Spectrum of Multi-Degree-of-Freedom Nonlinear Systems by a Galerkin Technique

G. Failla, Doctor of Philosophy,, P. D. Spanos, Fellow, ASME, M. Di Paola, Professor,
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Technical Papers
J. Appl. Mech. September 2003, 70(5): 708–714.
https://doi.org/10.1115/1.1599916
Published Online: October 10, 2003
View Article titled, Response Power Spectrum of Multi-Degree-of-Freedom Nonlinear Systems by a Galerkin Technique
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Topics: Computer simulation, Damping, Fourier series, Newton's method, Nonlinear systems, Polynomials, Spectral energy distribution, Jacobian matrices, Flow (Dynamics), Reliability
Journal Articles

Study of Frictional Impact Using a Nonsmooth Equations Solver

L. Johansson, A. Klarbring
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Technical Papers
J. Appl. Mech. June 2000, 67(2): 267–273.
https://doi.org/10.1115/1.1304825
Published Online: November 1, 1999
View Article titled, Study of Frictional Impact Using a Nonsmooth Equations Solver
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Topics: Algorithms, Computation, Equations of motion, Friction, Impulse (Physics), Newton's method, Coulomb's law, Nonlinear equations
Journal Articles

Dynamic Wrinkling of Viscoelastic Membranes

C. H. Jenkins, J. W. Leonard
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research Papers
J. Appl. Mech. September 1993, 60(3): 575–582.
https://doi.org/10.1115/1.2900841
Published Online: September 1, 1993
View Article titled, Dynamic Wrinkling of Viscoelastic Membranes
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Topics: Membranes, Cantilevers, Energy dissipation, Fatigue analysis, Finite element analysis, Newton's method, Stress, Waves
Journal Articles

The Effect of Shear Deformation on Post-Buckling Behavior of Laminated Beams

I. Sheinman, M. Adan
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research Papers
J. Appl. Mech. September 1987, 54(3): 558–562.
https://doi.org/10.1115/1.3173069
Published Online: September 1, 1987
View Article titled, The Effect of Shear Deformation on Post-Buckling Behavior of Laminated Beams
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Topics: Buckling, Shear deformation, Kinematics, Anisotropy, Composite materials, Newton's method, Nonlinear differential equations, Shear (Mechanics)
Journal Articles

An Iterative Numerical Solution for the Elastica With Causally Mixed Inputs

M. Hubbard
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Technical Briefs
J. Appl. Mech. March 1980, 47(1): 200–202.
https://doi.org/10.1115/1.3153607
Published Online: March 1, 1980
View Article titled, An Iterative Numerical Solution for the Elastica With Causally Mixed Inputs
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Topics: Deflection, Newton's method, Roads, Shapes
Journal Articles

Dynamic Buckling of the Elastic Cylindrical Shell Subjected to Impulsive Loading

W. F. Hubka
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research Papers
J. Appl. Mech. June 1974, 41(2): 401–406.
https://doi.org/10.1115/1.3423300
Published Online: June 1, 1974
View Article titled, Dynamic Buckling of the Elastic Cylindrical Shell Subjected to Impulsive Loading
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Topics: Buckling, Pipes, Dynamic response, Fourier series, Newton's method
Journal Articles

Floquet Theory and Newton’s Method

G. A. Thurston
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research Papers
J. Appl. Mech. December 1973, 40(4): 1091–1096.
https://doi.org/10.1115/1.3423131
Published Online: December 1, 1973
View Article titled, Floquet Theory and Newton’s Method
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Topics: Newton's method, Approximation, Computation, Differential equations, Nonlinear vibration, Numerical analysis
Journal Articles

The Application of Newton’s Method to the Problem of Elastic Stability

E. Riks
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research Papers
J. Appl. Mech. December 1972, 39(4): 1060–1065.
https://doi.org/10.1115/1.3422829
Published Online: December 1, 1972
View Article titled, The Application of Newton’s Method to the Problem of Elastic Stability
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Topics: Newton's method, Stability, Equilibrium (Physics)
Journal Articles

Large Deflections of a Linearly Viscoelastic Shallow Spherical Shell

A. L. Dea´k
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research Papers
J. Appl. Mech. June 1972, 39(2): 469–474.
https://doi.org/10.1115/1.3422702
Published Online: June 1, 1972
View Article titled, Large Deflections of a Linearly Viscoelastic Shallow Spherical Shell
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Topics: Buckling, Deflection, Deformation, Equilibrium (Physics), Newton's method, Pressure, Shallow spherical shells, Spherical shells, Stress
Journal Articles

A New Method for Computing Axisymmetric Buckling of Spherical Caps

G. A. Thurston
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research Papers
J. Appl. Mech. March 1971, 38(1): 179–184.
https://doi.org/10.1115/1.3408740
Published Online: March 1, 1971
View Article titled, A New Method for Computing Axisymmetric Buckling of Spherical Caps
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Topics: Buckling, Newton's method, Differential equations, Nonlinear differential equations, Pressure
Journal Articles

Discussion: “Continuation of Newton’s Method Through Bifurcation Points” (Thurston, G. A., 1969, ASME J. Appl. Mech., 36, pp. 425–430)

R. Schmidt, D. A. DaDeppo
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Discussions
J. Appl. Mech. March 1970, 37(1): 247.
https://doi.org/10.1115/1.3408476
Published Online: March 1, 1970
View Article titled, Discussion: “Continuation of Newton’s Method Through Bifurcation Points” (Thurston, G. A., 1969, ASME J. Appl. Mech., 36, pp. 425–430)
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Topics: Bifurcation, Newton's method
Journal Articles

Closure to “Discussion of ‘Continuation of Newton’s Method Through Bifurcation Points’” (1970, ASME J. Appl. Mech., 37, p. 247)

G. A. Thurston
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Discussions
J. Appl. Mech. March 1970, 37(1): 247–248.
https://doi.org/10.1115/1.3408477
Published Online: March 1, 1970
View Article titled, Closure to “Discussion of ‘Continuation of Newton’s Method Through Bifurcation Points’” (1970, ASME J. Appl. Mech., 37, p. 247)
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Topics: Bifurcation, Newton's method
Journal Articles

Continuation of Newton’s Method Through Bifurcation Points

G. A. Thurston
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research Papers
J. Appl. Mech. September 1969, 36(3): 425–430.
https://doi.org/10.1115/1.3564697
Published Online: September 1, 1969
View Article titled, Continuation of Newton’s Method Through Bifurcation Points
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Topics: Bifurcation, Newton's method, Nonlinear differential equations, Stability
Journal Articles

Approximate Analytical Solutions of the Finite-Deflection Equations for a Shallow Spherical Shell

A. Holston, Jr.
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research Papers
J. Appl. Mech. March 1967, 34(1): 65–72.
https://doi.org/10.1115/1.3607670
Published Online: March 1, 1967
View Article titled, Approximate Analytical Solutions of the Finite-Deflection Equations for a Shallow Spherical Shell
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Topics: Buckling, Deflection, Newton's method, Shallow spherical shells, Shells, Stress
Journal Articles

Discussion: “Newton’s Method Applied to Problems in Nonlinear Mechanics” (Thurston, G. A., 1965, ASME J. Appl. Mech., 32, pp. 383–388)

R. R. Archer
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Discussions
J. Appl. Mech. March 1966, 33(1): 234.
https://doi.org/10.1115/1.3625006
Published Online: March 1, 1966
View Article titled, Discussion: “Newton’s Method Applied to Problems in Nonlinear Mechanics” (Thurston, G. A., 1965, ASME J. Appl. Mech., 32, pp. 383–388)
Open the PDF for Discussion: “Newton’s Method Applied to Problems in Nonlinear Mechanics” (Thurston, G. A., 1965, ASME J. Appl. Mech., 32, pp. 383–388) in another window
Topics: Newton's method
Journal Articles

Closure to “Discussion of ‘Newton’s Method Applied to Problems in Nonlinear Mechanics’” (1966, ASME J. Appl. Mech., 33, p. 234)

G. A. Thurston
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Discussions
J. Appl. Mech. March 1966, 33(1): 234.
https://doi.org/10.1115/1.3625007
Published Online: March 1, 1966
View Article titled, Closure to “Discussion of ‘Newton’s Method Applied to Problems in Nonlinear Mechanics’” (1966, ASME J. Appl. Mech., 33, p. 234)
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Topics: Newton's method
Journal Articles

Newton’s Method Applied to Problems in Nonlinear Mechanics

G. A. Thurston
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research Papers
J. Appl. Mech. June 1965, 32(2): 383–388.
https://doi.org/10.1115/1.3625811
Published Online: June 1, 1965
View Article titled, Newton’s Method Applied to Problems in Nonlinear Mechanics
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Topics: Newton's method, Algebra, Boundary-value problems