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

Purpose – The purpose of this paper is to introduce a novel approach to solving linear systems arising from applying a Boundary Element Method (BEM) to elasticity problemsDesign/methodology/approach – The key idea is based on using wavelet transforms as a tool to change dense and fully populated matrices of BEM systems into sparse matrices Wavelets are then used again to produce an algorithm to solve the resultant sparse linear systems The wavelet transformation part of the method can be added as a black box to existing BEM codesFindings – Numerical results focusing on the sensitivity of the solution for various physical variables to the thresholding parameters, and savings in computer time and memory are presented The results show that the proposed method is efficient for large problemsResearch limitations/implications – Application of the proposed method is restricted to problems with number of DOF equal to an integer power of 2Originality/value – The novel algorithm to solve transformed algebrai

A novel way of using fast wavelet transforms to solve dense linear systems arising from boundary element methods

Study of sweetened seawater transportation by temperature difference.

Presenting new functions, basic displacement functions (BDFs), a novel method is introduced for the analysis of arbitrarily tapered thin plates in preference to primarily mathematically based methodologies. BDFs are obtained through applying unit load theorem and considering two orthogonal strips of unit width in tapered plates based on static deformations. It is shown that new shape functions and consequently structural matrices could be derived in terms of BDFs through a mechanical approach. On the other hand, BDFs could be used to calculate new shape functions, whereas Hermitian functions are used in several elements such as ACM and BFS. It is demonstrated that the accuracy of these new shape functions is significantly improved by considering the geometrical and mechanical properties of the plate element in the evaluation of the structural matrices. So, contrary to usual shape functions used in FE methods, they are susceptible to the thickness variation and then higher accuracy and more rapid convergence could be expected with fewer elements. In order to verify the competency of the proposed method, several numerical examples for classical boundary conditions are carried out and the results are compared with those in the literature.

Analysis of Tapered Thin Plates Using Basic Displacement Functions

Steel plate shear walls usually do not satisfy the strong-column weak-beam design criteria, leading to larger column sections. On the other hand, rigid frame structures are typically constructed in low-rise to mid-rise buildings built in locations prone to strong earthquakes due to their high flexibility and cost-effective solutions. Overcoming these restrictions to the SPSW system, this paper is dedicated to employing a semi-rigid connection that dissipates energy well and reduces the forces applied to the structure. By using a semi-rigid connection in an adjacent span to the SPSW, the actual flexural capacity of the beam end decreases and, subsequently, improves the performance of the structure in terms of the of the strong-column weak-beam criteria. Thereupon, the impact of the semi-rigid connections on steel frames with SPSWs as a sideway resisting system can be assessed by implementing a numerical study. In this paper, a new methodology for modelling semi-rigid joints is used considering five connections with different moment capacities. Moreover, the influence of three different circular diameters on the behavior of the perforated SPSWs was investigated. To fulfil these purposes, nonlinear dynamic analysis was conducted to assess the reliability of 5-, 10-, and 15-story frames resisted with SPSWs and semi-rigid connections subjected to actual ground motion records. A total of 45 frames were modelled and the obtained results were compared with reference benchmarks. The outcomes of the studies show good agreement with design building code requirements. In addition, the reliable performance of the structure under seismic loads is evaluated. According to the results of the parametric study, the presumed allowable drift leads to obtaining the optimum moment capacity of connection for each model and illustrates the applicability of a new structural system consisting of SPSWs and semi-rigid connections simultaneously. 

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On the Seismic Evaluation of Steel Frames Laterally Braced with Perforated Steel Plate Shear Walls Considering Semi-Rigid Connections

Since the accuracy of results obtained through displacement-based finite element method (FEM) considerably depends on the accuracy of shape functions used to interpolate the displacement field within an element, this paper aims at presenting a new efficient element for static and free vibration analysis of higher-order shear deformable beams using FEM with introducing basic displacement functions (BDFs). First, BDFs are introduced and computed. Afterward, new efficient shape functions are developed in terms of BDFs during the procedure based on the mechanical behavior of the element in which presented shape functions benefit generality and accuracy from stiffness and force method, respectively. Finally, deriving structural matrices of the beam with respect to new shape functions, static and free vibration behavior of the higher-order shear deformable beam is studied using FEM. The accuracy and economy of the method are demonstrated through several numerical examples.

Reza Attarnejad

Papers

A novel way of using fast wavelet transforms to solve dense linear systems arising from boundary element methods

Study of sweetened seawater transportation by temperature difference.

Analysis of Tapered Thin Plates Using Basic Displacement Functions

On the Seismic Evaluation of Steel Frames Laterally Braced with Perforated Steel Plate Shear Walls Considering Semi-Rigid Connections

On the FEM Analysis of Higher-Order Shear Deformable Beams: Validation of an Efficient Element