Miltiades Elliotis

Solving Laplacian problems with boundary singularities: a comparison of a singular function boundary integral method with the p/hp version of the finite element method

We solve a Laplacian problem over an L-shaped domain using a singular function boundary integral method as well as the p/hp finite element method. In the former method, the solution is approximated by the leading terms of the local asymptotic solution expansion, and the unknown singular coefficients are calculated directly. In the latter method, these coefficients are computed by post-processing the finite element solution. The predictions of the two methods are discussed and compared with recent numerical results in the literature.

A Singular Function Boundary Integral Method for Laplacian Problems with Boundary Singularities

A singular function boundary integral method for Laplacian problems with boundary singularities is analyzed. In this method, the solution is approximated by the truncated asymptotic expansion for the solution near the singular point and the Dirichlet boundary conditions are weakly enforced by means of Lagrange multiplier functions. The resulting discrete problem is posed and solved on the boundary of the domain, away from the point of singularity. The main result of this paper is the proof of convergence of the method; in particular, we show that the method approximates the generalized stress intensity factors, i.e., the coefficients in the asymptotic expansion, at an exponential rate. A numerical example illustrating the convergence of the method is also presented.

The singular function boundary integral method for an elastic plane stress wedge beam problem with a point boundary singularity

The singular function boundary integral method (SFBIM) is applied for the numerical solution of a 2-D Laplace model problem of a perfectly elastic wedge beam under plane stress conditions. The beam has a point boundary singularity, it includes a curved boundary part and is subjected to non-trivial distributed external loading. The implemented solution method converges for this special model problem extremely fast. The numerical estimates attained for the leading singular coefficients of the local asymptotic expansion and the stress and strain fields are highly accurate, as verified by comparison with the available analytical solution.

Implementing slack cables in the force density method

Purpose – The purpose of this paper is to present a solution strategy for the analysis of cable networks which includes an extension to the force density method (FDM) in an attempt to support cable elements when they become slack. The ability to handle slack cable elements in the analysis is particularly important especially in cases where the original cable lengths are predefined, i.e. the cable structure has already been constructed, and there is a need for further analysis to account for additional loading such as wind. The solution strategy is implemented in a software application. Design/methodology/approach – The development of the software required the implementation of the FDM for the analysis of cable networks and its extension to handle constraints. The implemented constraints included the ability to preserve the length in the stressed or the unstressed state of predefined cable elements. In addition, cable statics are incorporated with the development of the cable equation and its modification ...

The Singular Function Boundary IntegralMethod For A 3-D Laplacian ProblemWith An Edge Singularity

We developed the singular function boundary integral method for solving a 3-D Laplacian problem with an edge singularity. As in the case of 2-D problems, the solution is approximated by the leading terms of the local asymptotic solution expansion which are also used to weigh the governing equation in the Galerkin sense. The resulting discretised equations are reduced to boundary integrals by means of the divergence theorem. The Dirichlet boundary conditions are then weakly enforced by means of Lagrange multipliers. The values of the latter are calculated together with the so-called edge flux intensity functions, which appear in the local asymptotic solution. Our preliminary numerical results compare favourably with available post-processed finite element results for the same model problem.

Construction and Retrofit Methods of Stone Masonry Structures in Cyprus

Natural stone is a durable construction material which has been used through centuries for various types of structures. These structures are exposed to corrosive and degradation factors such as climate change and pollution, natural ageing, earthquake actions, increasing urbanization and even human negligence, potentially exposing them to irreversible structural damage and loss. Considering the large number of traditional structures and the historic value of a great number of stone masonry structures, the necessity of maintenance, repair, retrofit and restoration of stone masonry structures is imposed. The process which leads to the preservation of such structures consists of three stages: 1) the in-situ and laboratory study of the degree of damage and of the factors which cause the natural damages on the materials of these buildings, 2) the detailed drawing of the layout and the elevations. This stage also includes the selection of the appropriate measures for the maintenance and retrofits according to the special characteristics of the structure and the design of the intervention method, and 3) the execution of all the intervention works. This paper presents a description of various types of natural stones found in Cyprus, the most commonly used construction methods as well as methods for the retrofit of stone masonry structures.

Analysis of Tensegrity Structures with Redundancies, by Implementing a Comprehensive Equilibrium Equations Method with Force Densities

A general approach is presented to analyze tensegrity structures by examining their equilibrium. It belongs to the class of equilibrium equations methods with force densities. The redundancies are treated by employing Castigliano’s second theorem, which gives the additional required equations. The partial derivatives, which appear in the additional equations, are numerically replaced by statically acceptable internal forces which are applied on the structure. For both statically determinate and indeterminate tensegrity structures, the properties of the resulting linear system of equations give an indication about structural stability. This method requires a relatively small number of computations, it is direct (there is no iteration procedure and calculation of auxiliary parameters) and is characterized by its simplicity. It is tested on both 2D and 3D tensegrity structures. Results obtained with the method compare favorably with those obtained by the Dynamic Relaxation Method or the Adaptive Force Density Method.