Application of Discrete Finite Element Method for Analysis of Unreinforced Masonry Structures

2016 ◽  
pp. 440-458
Author(s):  
Iraj H. P. Mamaghani
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Study ◽  
Yield Criterion ◽  
Unreinforced Masonry ◽  
Masonry Structures ◽  
Linear Behavior ◽  
Secant Stiffness ◽  
Discrete Finite Element ◽  
Element Method

In this chapter, through some illustrative examples, the applicability of the Discrete Finite Element Method (DFEM) to analysis of unreinforced masonry structures such as rock pillars, open rock slopes, underground openings, tunnels, fault propagations, and fault-structure interactions is examined and discussed. In the numerical study, the behavior of contacts and blocks is assumed to be elasto-plastic or elastic. The Mohr-Coulomb yield criterion, representing material behavior of contacts, is implemented in the developed codes for DFEM used in the analysis. The secant stiffness method with the updated Lagrangian scheme is employed to deal with non-linear behavior. The constant strain triangular element with two degrees of freedoms at each node, formed by properly joining the corners and contact nodes of an individual block, is adopted for finite element meshing of the blocks. The DFEM provides an efficient and promising tool for designing, analyzing, and studying the behavior of unreinforced masonry structures.

Discrete Finite Element Method Application for Analysis of Unreinforced-Masonry Underground Structures

2015 ◽  
Vol 2522 (1) ◽  
pp. 131-136 ◽  
Author(s):  
Iraj H. P. Mamaghani
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Discrete Systems ◽  
Unreinforced Masonry ◽  
Continuous Systems ◽  
Underground Structures ◽  
Interface Elements ◽  
Underground Openings ◽  
Discrete Finite Element ◽  
Element Method

Unreinforced-masonry underground structures are composed of a finite number of distinct interacting blocks that have length scales relatively comparable with the underground openings of interest. Therefore, these structures are ideal candidates for modeling as discrete systems instead of as continuous systems. The discrete finite element method (DFEM) developed by the author to model discontinuous media consisting of blocks of arbitrary shapes was adopted for the static analysis of unreinforced masonry underground structures. The developed DFEM was based on the principles of the finite element method incorporating contact elements. The DFEM considers blocks as subdomains and represents them by solid elements. Contact elements, which are far superior to joint or interface elements, are used to model block interactions such as sliding or separation. In this study, the DFEM is briefly reviewed; then, through some illustrative examples, the applicability of the DFEM to the analysis of unreinforced-masonry underground structures is examined and discussed. It is shown that the DFEM provides an efficient tool for researchers and practical engineers in designing, analyzing, and studying the behavior of unreinforced masonry underground structures under static loading.

Discrete Finite Element Method for Analysis of Masonry Structures

2016 ◽  
pp. 393-415
Author(s):  
Iraj H. P. Mamaghani
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Discrete Systems ◽  
Masonry Structures ◽  
Static And Dynamic Analysis ◽  
Underground Openings ◽  
Dynamic Loadings ◽  
Arch Bridges ◽  
Discrete Finite Element ◽  
Element Method

Masonry structures are comprised of a finite number of distinct interacting rock blocks that have a length scale relatively comparable to the structure. Therefore, they are ideal candidates for modeling as discrete systems. This chapter covers the Discrete Finite Element Method (DFEM) developed by the author to model discontinuous media consisting of blocks of arbitrary shapes. The DFEM is based on the finite element method incorporating contact elements. The DFEM considers blocks as sub-domains and represents them as solid elements. Contact elements are used to model block interactions such as sliding or separation. In this chapter, through some illustrative examples, the applicability of the DFEM to static and dynamic analysis of masonry structures, including arch bridges, walls, slopes, and underground openings, is discussed. The DFEM provides an efficient tool for researchers and practical engineers in designing, analyzing, and studying the behavior of masonry structures under static and dynamic loadings.

scholarly journals Numerical study of Fisher's equation by a Petrov-Galerkin finite element method

1991 ◽  
Vol 33 (1) ◽  
pp. 27-38 ◽  
Author(s):  
S. Tang ◽  
R. O. Weber
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Study ◽  
Galerkin Finite Element Method ◽  
Linear Diffusion ◽  
Galerkin Finite Element ◽  
Fisher’S Equation ◽  
Nonlinear Reaction ◽  
Fisher's Equation ◽  
Element Method

AbstractFisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by a Petrov-Galerkin finite element method. The results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are determined by the system itself and are independent of the initial values. Comparing with other studies, the numerical scheme used in this paper is satisfactory with regard to its accuracy and stability. It has the advantage of being much more concise.

The Semi-Discrete Finite Element Method for the Cauchy Equation

2014 ◽  
Vol 668-669 ◽  
pp. 1130-1133
Author(s):  
Lei Hou ◽  
Xian Yan Sun ◽  
Lin Qiu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Results ◽  
Cauchy Equation ◽  
The Time Domain ◽  
Nicolson Scheme ◽  
Discrete Finite Element ◽  
Better Than ◽  
Element Method ◽  
Crank Nicolson

In this paper, we employ semi-discrete finite element method to study the convergence of the Cauchy equation. The convergent order can reach. In numerical results, the space domain is discrete by Lagrange interpolation function with 9-point biquadrate element. The time domain is discrete by two difference schemes: Euler and Crank-Nicolson scheme. Numerical results show that the convergence of Crank-Nicolson scheme is better than that of Euler scheme.

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