This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

Structural dynamics: VonGyörgy Vértes. Amsterdam: Elsevier Science Publishers 1985. 320 S., US $72.25

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them.
Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ different methods such as series expan- sion, linear programming, linear matrix inequalities, collocation methods, al- gebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function.

https://www.aimsciences.org/article/exportPdf?id=ee7e4111-9a13-4e44-95c8-14c5557278fc

Review on computational methods for Lyapunov functions

Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm

Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements

To design a steel shear wall, dynamics of stress concentration on the columns and beam under lateral loads is essential. Therefore, it has been suggested that the thickness of plates should be redu...

Study on the seismic behaviour of steel shear plates

A formula for calculating fundamental natural frequency of partially-filled tanks

Many triangular elements have been formulated for bending plate analysis so far. In this type of element, researchers generally considered the same distance between the side nodes. The present study will show that these types of node locations are not the best. To clarify the effect of side node locations, three new triangular elements will be formulated for the analysis of thin bending plates. These are nonconforming elements and have 10, 15, and 21 degrees of freedom, respectively. Merits and disadvantages of these proposed elements will be revealed by solving different structures. Optimal side nodes' location will be positioned by changing the place of element nodes. Numerical tests will confirm that element accuracy in the best possible situation is much better than the state in which side nodes have the same distance. Moreover, this study will reveal that the presented optimal locations of nodes have no significant dependence on the load cases, boundary conditions, distortion of element shape, and variation of the meshes.

Optimal node location in triangular plate bending elements

A rectangular plane element containing an internal open stable crack is formulated. Using the well-known local flexibility approach, the element flexibility matrix is derived by the addition of the...

Mohammad Rezaiee-Pajand

Papers

Study on the seismic behaviour of steel shear plates

A formula for calculating fundamental natural frequency of partially-filled tanks

Optimal node location in triangular plate bending elements

A Force-Based Rectangular Cracked Element

A family of cylindrical elements