A direct numerical method for solving the Föppl-Hencky equation

2019 ◽  
Author(s):  
Min Zhao ◽  
Xiaoping Zhang ◽  
Yongping Sun
Keyword(s):  
Numerical Method ◽  
Direct Numerical Method

The numerical solution of the heat conduction equation in one dimension

1964 ◽  
Vol 60 (4) ◽  
pp. 897-907 ◽  
Author(s):  
M. Wadsworth ◽  
A. Wragg
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Heat Conduction Equation ◽  
Linear Equations ◽  
Conduction Equation ◽  
Partial Differential ◽  
Direct Numerical Method

AbstractThe replacement of the second space derivative by finite differences reduces the simplest form of heat conduction equation to a set of first-order ordinary differential equations. These equations can be solved analytically by utilizing the spectral resolution of the matrix formed by their coefficients. For explicit boundary conditions the solution provides a direct numerical method of solving the original partial differential equation and also gives, as limiting forms, analytical solutions which are equivalent to those obtainable by using the Laplace transform. For linear implicit boundary conditions the solution again provides a direct numerical method of solving the original partial differential equation. The procedure can also be used to give an iterative method of solving non-linear equations. Numerical examples of both the direct and iterative methods are given.

Contact analysis of road aggregate with friction using a direct numerical method

Wear ◽  
2010 ◽  
Vol 268 (5-6) ◽  
pp. 686-692 ◽  
Author(s):  
Julien Cesbron ◽  
Hai Ping Yin
Keyword(s):  
Numerical Method ◽  
Contact Analysis ◽  
Direct Numerical Method

scholarly journals Analyzing the Departure Runway Capacity Effects of Integrating Optimized Continuous Climb Operations

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Manuel Villegas Díaz ◽  
Fernando Gómez Comendador ◽  
Javier García-Heras Carretero ◽  
Rosa María Arnaldo Valdés
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Numerical Method ◽  
Optimal Control Theory ◽  
Fast Time ◽  
Environmental Footprint ◽  
Time Simulation ◽  
Direct Numerical Method ◽  
Operational Technique ◽  
Potential Applicability

Performing Continuous Climb Operation (CCO) procedures enable the reduction of the environmental footprint and the improvement of the trajectory efficiency when individually operated. However, its operation may affect negatively the overall operational efficiency at Terminal Manoeuvring Areas (TMAs). The estimation of capacity is a matter of paramount importance to all airport planning and analyzing the capacity effects of this particular operational technique on a certain scenario will definitely help on evaluating its potential applicability. In this paper, departure runway capacity at the Adolfo Suárez Madrid-Barajas airport was operationally evaluated when introducing CCOs. The considered trajectories consisted of multiobjective optimized CCOs based on the optimal control theory, using the pseudospectral direct numerical method. These scenarios allowed addressing of the incremental variations of CCOs versus conventional departures, through fast time simulation, with the objective to assess the effects on the operations.

In-Plane Wave Propagation Through Elastic Solids With a Periodic Array of Rectangular Defects

2001 ◽  
Vol 69 (2) ◽  
pp. 179-188 ◽  
Author(s):  
E. Scarpetta ◽  
M. A. Sumbatyan
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Numerical Method ◽  
Analytical Approach ◽  
Complete Solution ◽  
Periodic Array ◽  
Elastic Solids ◽  
Longitudinal Plane ◽  
Direct Numerical Method ◽  
Plane Wave Propagation

In the context of wave propagation in damaged (elastic) solids, an analytical approach is developed to study normal penetration of a longitudinal plane wave into a periodic array of rectangular defects. Reducing the problem to some integral equations holding over the base and height of the openings, a direct numerical method is applied to give a complete solution for various exact or approximated forms. Several figures show the peculiarities of the structure and lead to physical conclusions.

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