There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

Shape-Memory Materials

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Seismic Design Of Reinforced Concrete And Masonry Buildings

Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory

This paper assesses three definitions of eccentricity employed in the description of asymmetric multistory buildings. Other definitions of static eccentricity in multistory buildings fall essentially into one of the above categories. Using the three approaches, formulae are developed to evaluate the asymmetry of shear-type buildings where the deformation is governed by the lateral and rotational rigid-floor displacements arising from the seismic design loadings. Finally by modelling three concrete buildings according to Iranian concrete code (ABA) and investigating these three definitions and comparing them, the best method for representing Iranian 2800 Standard was selected.  Simple comparisons and comments on the alternative approaches are presented with the aid of these appropriate examples. This clarification of the definition of eccentricity is needed for improved understanding of the application of codified torsional design procedures. It is also a prerequisite for advanced studies of the inelastic seismic response of multistory shear buildings.

Structural Eccentricity Evaluation in Iranian 2800 Standard (Technical Note)

Aquifer feature estimation in Basara basin using a groundwater modeling system for smart agriculture

Abstract. In recent years several researches have been done on different ways of analyzing and designing arch dams but most of them were involved with cumbersome calculations and heavy loads of computations. In this paper a novel approach for dynamic analysis of arch dams is presented. The most commonly accepted method for analyzing arch dams assumes that the horizontal water load is divided between arches and cantilevers so that the arch and cantilever deflections are equal at conjugate points in all parts of structure. In this the arch dam is modeled as non-prismatic curved beam resting on continues elastic foundation. Based on structural and mechanical principals, a flexibility based method is used to evaluate exact structural matrices and by introducing the concept of basic displacement functions (BDFs), it is shown that dynamic shape functions are derived in terms of BDFs. The flexibility basis ensures the true satisfaction of equilibrium equations at any interior point of the curved element. Dynamic stiffness matrix is evaluated by solving the governing equation of motion. Differential Transform method, a powerful numerical tool in solving of ordinary differential equations, is used for this purpose. The method is capable of modeling any curved element whose crosssectional area and moment of inertia vary along beam with any two arbitrary functions and any type of cross-section with just few numbers of elements so that it can be used in most of engineering applications concerning non-prismatic curved beams and arch dams in particular. In order to verify the competency of the method, a numerical example are presented and the results and convergence of them are compared with other methods in the literature.

Basic displacement functions in dynamic analysis of an arch dam as a curved beam resting on a continues elastic foundation

An innovative procedure for choosing the Primary Structure used in the flexibility method of analysis is presented for plane truss problems. An intelligent algorithm for determining the redundancies is developed based on the definition of fixed joints of the structure, hence the method is called "Fixed Nodes Method". The local stability of the nodes is guaranteed and for most trusses the global stability is maintained; the rest of the members are known as redundant. Several examples show the good performance of this method.

Automatic choice of redundancies in the force method of analysis

This paper presents the formulation of a new efficient and conforming rectangular finite element for analysis of thin plates with any arbitrary variation of thickness along both edges. Shape functions of this new element are derived from multiplying shape functions of non-prismatic Euler–Bernoulli beam extracted from basic displacement functions. To provide [Formula: see text] consistency along the edges of elements, twist is added to conventional degrees of freedom, namely deflection and slopes resulting in an element with 16 degrees of freedom. The proposed element is used to solve various static and dynamic problems, and it is seen that the convergence of a new formulation occurs with much fewer elements compared to existing finite elements as a direct result of considering the variation of geometry in the derivation of shape functions, which renders the formulation competitive in both exactness and economy.

Reza Attarnejad

Papers

Structural Eccentricity Evaluation in Iranian 2800 Standard (Technical Note)

Aquifer feature estimation in Basara basin using a groundwater modeling system for smart agriculture

Basic displacement functions in dynamic analysis of an arch dam as a curved beam resting on a continues elastic foundation

Automatic choice of redundancies in the force method of analysis

A New Rectangular Finite Element for Static and Dynamic Analysis of Arbitrarily Tapered Plates