A Review on linear dynamic analysis by Dual Reciprocity Boundary Element Method

Analyzing the problems related to the phenomenon of wave propagation and finding optimal methods to solve it are among the important issues that have been highly regarded by earthquake engineering researchers in recent decades. Major studies related to earthquake effects on seismic sites have shown that the effects of earthquake waves on the site are mainly due to factors such as the type and angle of the impact wave, intensity, duration and frequency content of the wave and site characteristics such as surface topography and soil layering properties. The development of new equations of wave propagation by considering each of these characteristics is important and over the past years researchers have proposed new methods to solve them. The most important methods in studying the wave propagation phenomenon can be divided into three categories: laboratory methods, physical modeling and mathematical modeling. Laboratory methods are largely consistent with the physical nature of the problems, and their results are more accurate than other methods. Methods such as direct wave propagation on soil, resonance column method and piezoelectric method are among the most important laboratory methods in the study of wave propagation phenomenon. However, these methods mainly require the use of precision hardware equipment, which is not always available and their use is not always cost-effective. On the other hand the mathematical modeling is important. In this category, the most correct equations governing the wave propagation phenomenon are extracted and then solved. The most important advantage of mathematical modeling methods is that, they are more cost-effective and the results of their procedures can be extracted very fast. Based on governing equations the mathematical modeling can be categorized into analytical and numerical methods. In the past, when precise computational tools were not available, the governing equations of each physical phenomenon were solved by considering simple boundary and initial conditions, and formulated answers were only presented to that simple problem. These types of answers are known as analytical solutions. The most important issue of this type of solutions is the lack of accurate answers when other complex problems are considered, so that it is necessary to provide accurate analytical answers again for problems with complex boundary and geometric conditions. In the early twentieth century, with the growth and development of computers and computing tools, another type of method called numerical methods was developed. In this method, by discretizing the environment into small components called elements, and applying approximate equations to each component, an attempt is made to obtain an approximate answer to the problem. Numerical methods can be divided into two categories based on the type of discretization: volumetric methods and boundary methods. Unlike volumetric methods, in which discretization is mainly performed on the domain of the environment, in boundary methods, discretization is mainly performed on the boundaries of the environment. For this reason, the computational efforts in boundary methods is significantly less than volumetric methods and more accurate results can be achieved by spending less computational power. In this research, after reviewing the technical literature and research on the development of boundary methods in modeling the wave propagation phenomenon, then the dual reciprocity boundary element method as one of the most widely used branches of boundary methods will be reviewed. Finally, by carefully reviewing the researches, an attempt has been made to report the shortcomings and unknown points of boundary methods in order to promote future researches.