On the Nonlinear Intrinsic Dynamics of Doubly Curved Shells

1981 ◽  
Vol 48 (4) ◽  
pp. 909-914 ◽  
Author(s):  
A. Libai
Keyword(s):  
Equations Of Motion ◽  
Time Integration ◽  
Constant Load ◽  
Field Equations ◽  
Integration Schemes ◽  
Doubly Curved Shells ◽  
External Reference ◽  
Time Integration Schemes ◽  
Intrinsic Form ◽  
Doubly Curved

The field equations of motion and compatibility for the nonlinear dynamics of doubly curved shells are recast in an intrinsic form, in terms of the metric and curvature functions of their reference surfaces. For appropriate input, the motion of the shell is described without the need for an external reference coordinate system or the use of vector quantities such as position, velocity, and acceleration. The equations are shown to be readily applicable to time integration schemes. Such cases, as the (spatially) constant load problem and the inextensional dynamics problem, are also considered. The need for further work in the area is emphasized.

scholarly journals Damping Acoustic Modes in Compressible Horizontally Explicit Vertically Implicit (HEVI) and Split-Explicit Time Integration Schemes

2018 ◽  
Vol 146 (6) ◽  
pp. 1911-1923 ◽  
Author(s):  
Joseph B. Klemp ◽  
William C. Skamarock ◽  
Soyoung Ha
Keyword(s):  
Acoustic Waves ◽  
Acoustic Noise ◽  
Equations Of Motion ◽  
Time Integration ◽  
Time Step ◽  
Explicit Time Integration ◽  
Physical Interest ◽  
Acoustic Modes ◽  
Integration Schemes ◽  
Time Integration Schemes

Although the equations of motion for a compressible atmosphere accommodate acoustic waves, these modes typically play an insignificant role in atmospheric processes of physical interest. In numerically integrating the compressible equations, it is often beneficial to filter these acoustic modes to control acoustic noise and prevent its artificial growth. Here, a new technique is proposed for filtering the 3D divergence that may damp acoustic modes more effectively than filters previously implemented in numerical modes using horizontally explicit vertically implicit (HEVI) and split-explicit time integration schemes. With this approach, a divergence damping term is added as a final adjustment to the horizontal velocity at the new time level after completing the vertically implicit portion of the time step. In this manner, the divergence used in the filter term has exactly the same numerical form as that used in the discrete pressure equation. Analysis of the dispersion equation for this form of the filter documents its stability characteristics and confirms that it effectively damps acoustic modes with little artificial influence on the amplitude or propagation of the gravity wave modes that are of physical interest. Some specific aspects of the implementation of the filter in the Model for Prediction Across Scales (MPAS) are discussed, and results are presented to illustrate some of the beneficial aspects of suppressing acoustic noise.

Rational derivation of conserving time integration schemes

2008 ◽  
pp. 149-164
Author(s):  
Elias Paraskevopoulos ◽  
Christos Panagiotopoulos ◽  
Demosthenes Talaslidis
Keyword(s):  
Time Integration ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Conserving Time Integration

scholarly journals Damaged behavior under plane stress

2011 ◽  
pp. 341-368
Author(s):  
Thomas Paris ◽  
Khémaïs Saanouni
Keyword(s):  
Plane Stress ◽  
Constitutive Equations ◽  
Stress Condition ◽  
Time Integration ◽  
Reference Case ◽  
Plane Stress Condition ◽  
Integration Schemes ◽  
Hyperbolic Sine ◽  
Time Integration Schemes ◽  
Fully Coupled

This paper deals with the numerical treatment of "advanced" elasto-viscoplasticdamage constitutive equations in the particular case of plane stress. The viscoplastic constitutive equations account for the mixed isotropic and kinematic non linear hardening and are fully coupled with the isotropic ductile damage. The viscous effect is indifferently described by a power function (Norton type) or an hyperbolic sine function. Different time integration schemes are used and compared to each other assuming plane stress condition, widely used when dealing with shell structures as well as to the 3D reference case.

3D nonlinear MHD calculations using implicit and explicit time integration schemes

1986 ◽  
Vol 65 (2) ◽  
pp. 253-272 ◽  
Author(s):  
L. Garcia ◽  
H.R. Hicks ◽  
B.A. Carreras ◽  
L.A. Charlton ◽  
J.A. Holmes
Keyword(s):  
Time Integration ◽  
Explicit Time Integration ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Implicit And Explicit
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