scholarly journals T-Splines for Isogeometric Analysis of Two-Dimensional Nonlinear Problems

2020 ◽  
Vol 123 (2) ◽  
pp. 821-843
Author(s):  
Mayi Guo ◽  
Gang Zhao ◽  
Wei Wang ◽  
Xiaoxiao Du ◽  
Ran Zhang ◽  
...  
Keyword(s):  
Isogeometric Analysis ◽  
Nonlinear Problems ◽  
Two Dimensional

Dynamic Response of Surface-Moored Vertical Barrier to Wave Action by Analog and Digital Simulation

1974 ◽  
Vol 96 (1) ◽  
pp. 335-342
Author(s):  
J. R. Fowler ◽  
E. I. Bailey
Keyword(s):  
Theoretical Model ◽  
Digital Simulation ◽  
Nonlinear Problems ◽  
Analog Computer ◽  
Two Dimensional ◽  
Test Program ◽  
Analog Simulation ◽  
Vertical Barrier ◽  
Amplitude Data ◽  
Lab Test

The two-dimensional dynamics of an oil containment barrier, which was designed to have very low tensile loads due to current and waves, were simulated with a theoretical model. The model was solved on both analog and digital computers, and a lab test program conducted to verify the model. For nonlinear problems such as this, for which “exact” solutions do not exist, the analog computer has many advantages, principally rapid parameter studies and convenient plotting output, plus giving the engineer a real time “feel” for the problem. The problem treated here was especially well-suited to analog simulation. Charts and graphs present maximum force and amplitude data, and experimental verification of the solution was obtained from wave tank studies.

Application of Process Analysis Method to the Solution of 2-DNonlinear Progressive Gravity Waves

1992 ◽  
Vol 36 (01) ◽  
pp. 30-37
Author(s):  
S. J. Liao
Keyword(s):  
Gravity Waves ◽  
Process Analysis ◽  
Perturbation Expansion ◽  
Continuous Mapping ◽  
Nonlinear Problems ◽  
Expansion Method ◽  
Order Of Approximation ◽  
Two Dimensional ◽  
Analysis Method ◽  
Perturbation Expansion Method

Based on continuous mapping, a kind of analytical method for nonlinear problems, namely, the Process Analysis Method, is described and used to solve two-dimensional nonlinear progressive gravity waves. Solutions at the fourth order of approximation are obtained and compared with Stokesian waves. In contrast to the perturbation expansion method, the Process Analysis Method is independent of small or great parameters and therefore can solve nonlinear problems without small or great parameters.

Boundary tracing and boundary value problems: I. Theory

2007 ◽  
Vol 463 (2084) ◽  
pp. 1909-1924 ◽  
Author(s):  
Michael L Anderson ◽  
Andrew P Bassom ◽  
Neville Fowkes
Keyword(s):  
Differential Equation ◽  
Nonlinear Problems ◽  
Boundary Curve ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Partial Differential ◽  
Boundary Constraints ◽  
Linear And Nonlinear ◽  
Boundary Tracing ◽  
Analytical Tools

Given an exact solution of a partial differential equation in two dimensions, which satisfies suitable conditions on the boundary of the domain of interest, it is possible to deform the boundary curve so that the conditions remain fulfilled. The curves obtained in this manner can be patched together in various ways to generate a remarkably broad range of domains for which the boundary constraints remain satisfied by the initial solution. This process is referred to as boundary tracing and works for both linear and nonlinear problems. This article presents a general theoretical framework for implementing the technique for two-dimensional, second-order, partial differential equations with a general flux condition imposed around the boundary. A couple of simple examples are presented that serve to demonstrate the analytical tools in action. Applications of more intrinsic interest are discussed in the following paper.

Sign in / Sign up

Export Citation Format

Share Document