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Author: Min Nan Tseng Publisher: ISBN: Category : Difference equations Languages : en Pages : 250
Book Description
The object of this study is to develop a transmitting boundary suitable for use in numerical solution of wave propagation problems. The detailed analysis refers to two-dimensional problems in plane strain. The medium near the transmitting boundaries must be linear, but inelastic action is permitted within the region. The method consists first of splitting the field near the boundaries into its irrotational (P) and equivoluminal (S) components by finding potentials for the motion near the boundaries. Transmitting boundaries are then developed which pass P and S waves with no interaction. Two types of transmitting boundary have been devised. In the first, the disturbances are taken as locally plane near the boundary in each time interval. A more refined approximation is also obtained in which the disturbances are taken as locally cylindrical. Numerical comparisons have been carried out which indicate that these transmitting boundaries actually perform well and are suitable for practical computation. In addition, other boundary conditions are examined by the use of potentials, especially the boundary between two elastic layers with different properties. Calculations show that the numerical solutions in the vicinity of such a boundary are stable, unlike the results obtained in some earlier work which did not use potentials.
Author: Min Nan Tseng Publisher: ISBN: Category : Difference equations Languages : en Pages : 250
Book Description
The object of this study is to develop a transmitting boundary suitable for use in numerical solution of wave propagation problems. The detailed analysis refers to two-dimensional problems in plane strain. The medium near the transmitting boundaries must be linear, but inelastic action is permitted within the region. The method consists first of splitting the field near the boundaries into its irrotational (P) and equivoluminal (S) components by finding potentials for the motion near the boundaries. Transmitting boundaries are then developed which pass P and S waves with no interaction. Two types of transmitting boundary have been devised. In the first, the disturbances are taken as locally plane near the boundary in each time interval. A more refined approximation is also obtained in which the disturbances are taken as locally cylindrical. Numerical comparisons have been carried out which indicate that these transmitting boundaries actually perform well and are suitable for practical computation. In addition, other boundary conditions are examined by the use of potentials, especially the boundary between two elastic layers with different properties. Calculations show that the numerical solutions in the vicinity of such a boundary are stable, unlike the results obtained in some earlier work which did not use potentials.
Author: A. H. -S. Ang Publisher: ISBN: Category : Languages : en Pages : 162
Book Description
A numerical discrete-element method of wave motion analysis is summarized and extended for problems involving infinite or semi-infinite solid media in plane and axi-symmetric conditions. Space discretization of a solid medium is accomplished through a lumped-parameter discrete-element model of the medium, whereas the time discretization is embedded within a general numerical integrator. This invariably leads to a system of finite difference equations; thus, the required mathematical conditions for numerical stability can be developed on the basis of available finite difference theory. Explicit stability conditions for plane and axi-symmetric problems are presented. Calculations of wave motions in an infinite or semi-infinite space can be confined to a finite region or interest if the region is terminated by suitable transmitting boundaries such that no significant reflections are generated at these artificial boundaries. Based on the concept of a step-wise transmission of D'Alembert forces, a general transmitting boundary was developed for the discrete-element method of analysis. The boundary was verified extensively through actual calculations of plane strain and axi-symmetric problems, including those with layered half-spaces, elastic-plastic systems, and a problem involving long calculation time. (Author).
Author: C.A. Brebbia Publisher: Springer Science & Business Media ISBN: 9400961928 Category : Mathematics Languages : en Pages : 442
Book Description
This book constitutes the edited proceedings of the Advanced Studies Institute on Boundary Element Techniques in Computer Aided Engineering held at The Institute of Computational Mechanics, Ashurst Lodge, Southampton, England, from September 19 to 30, 1984. The Institute was held under the auspices of the newly launched "Double Jump Programme" which aims to bring together academics and industrial scientists. Consequently the programme was more industr ially based than other NATO ASI meetings, achieving an excellent combination of theoretical and practical aspects of the newly developed Boundary Element Method. In recent years engineers have become increasingly interested in the application of boundary element techniques for'the solution of continuum mechanics problems. The importance of boundary elements is that it combines the advantages of boundary integral equations (i.e. reduction of dimensionality of the problems, possibility of modelling domains extending to infinity, numerical accura'cy) with the versatility of finite elements (i.e. modelling of arbitrary curved surfaces). Because of this the technique has been well received by the engineering and scientific communities. Another important advantage of boundary elements stems from its reduction of dimensionality, that is that the technique requires much less data input than classical finite elements. This makes the method very well suited for Computer Aided Design and in great part explains the interest of the engineering profession in the new technique.
Author: A.S. Cakmak Publisher: Elsevier ISBN: 0444600469 Category : Science Languages : en Pages : 633
Book Description
Despite advances in the field of geotechnical earthquake engineering, earthquakes continue to cause loss of life and property in one part of the world or another. The Third International Conference on Soil Dynamics and Earthquake Engineering, Princeton University, Princeton, New Jersey, USA, 22nd to 24th June 1987, provided an opportunity for participants from all over the world to share their expertise to enhance the role of mechanics and other disciplines as they relate to earthquake engineering. The edited proceedings of the conference are published in four volumes. This volume covers: Seismicity and Tectonics in the Eastern Mediterranean, Seismic Waves in Soils and Geophysical Methods, Engineering Seismology, Dynamic Methods in Soil and Rock Mechanics, and Ground Motion. With its companion volumes, it is hoped that it will contribute to the further development of techniques, methods and innovative approaches in soil dynamics and earthquake engineering.
Author: C. A. Brebbia Publisher: Springer ISBN: Category : Science Languages : en Pages : 286
Book Description
As the Boundary Element Method develops into a tool of engineering analysis more effort is dedicated to studying new applications and solving different problems. This book contains chapters on the basic principles of the technique, time dependent problems, fluid mechanics, hydraulics, geomechanics and plate bending. The number of non-linear and time dependent problems which have become amenable to solution using boundary elements have induced many researchers to investigate in depth the basis of the method. Chapter 0 of this book presents an ap proach based on weighted residual and error approximations, which permits easy construction of the governing boundary integral equations. Chapter I reviews the theoretical aspects of integral equation formulations with emphasis in their mathematical aspects. The analysis of time dependent problems is presented in Chap. 2 which describes the time and space dependent integral formulation of heat conduction problems and then proposes a numerical procedure and time marching algorithm. Chapter 3 reviews the application of boundary elements for fracture mechanics analysis in the presence of thermal stresses. The chapter presents numerical results and the considerations on numerical accuracy are of interest to analysts as well as practising engineers.
Author: William Yeung Publisher: ISBN: Category : Languages : en Pages : 50
Book Description
The purpose of this effort was to study the construction of novel energy absorbing boundary conditions for use at the artificial far field boundaries of exterior wave problems. One approach was pursued which involves the superposition of the solutions for a fixed boundary and for a free boundary. An analytic model was used to identify the cause of the small errors that result in the cancellation process of this approach. This model showed that the appropriate velocity at the free boundary has to be modified when the computational time step is less than the maximum stable time step. First and second order corrections have been developed.
Author: Min Nan Tseng
Author: Min Nan Tseng
Author: 
Author: Institute for Computer Applications in Science and Engineering
Author: Shahid Ahmad
Author: U.S. Nuclear Regulatory Commission
Author: A. H. -S. Ang
Author: C.A. Brebbia
Author: A.S. Cakmak
Author: C. A. Brebbia
Author: William Yeung