AN INNOVATIVE BOUNDARY ELEMENT FORMULATION FOR BUILDING SLABS

Slab supported by beams (i.e. beam-slab floor) is a common practice in the construction of buildings. Modeling this slab type using the boundary element method (BEM) is an essential step to provide seamless frameworks for the analysis of buildings with complex geometries. However, one of the most challenging difficulties that have been facing research efforts in this area is its theoretical setting with limited applicability to practical building slabs. This limitation is addressed in this research work and a practical BEM-based formulation for the slab-beam floor is presented. The presented formulation discretizes the connection area between the slab, and beams and columns into cells (supporting cells). The centroids of these cells are used to carry out an additional collocation scheme which is required to solve the resulting system of equations. To generate the slab stiffness matrix, the generalized displacements that correspond to the supporting cells’ degrees of freedom are set to unity (one at a time). By assembling the generated slab stiffness matrix with beams and columns stiffness matrices using the stiffness analysis method, the overall stiffness matrix is obtained. Hooke’s law is then applied to calculate the generalized displacements and straining actions are obtained in the post-processing phase. The developed formulation is applied to an example to validate its results by comparing it with the analytical solution.

Stress state of hinged supported thin-wall elastic structures

The paper studies the stress-strain state of flat elastic isotropic thin-walled shell structures in the framework of the S. P. Timoshenko shear model with pivotally supported edges. The stress-strain state of shell structures is described by a system of five second-order nonlinear partial differential equations under given static boundary conditions with respect to generalized displacements. The system of equations under study is linear in terms of tangential displacements, rotation angles, and nonlinear in terms of normal displacement. To find a solution to the system that satisfies the given static boundary conditions, integral representations for generalized displacements containing arbitrary holomorphic functions are used. Finding holomorphic functions is one of the main and difficult points in the proposed study. The integral representations constructed in this way allow us to reduce the original problem to a single nonlinear operator equation with respect to the deflection, the solvability of which is established using the principle of compressed maps.

Strength of thin-walled elastic building structures

The existence theorem is proved within the framework of the shear model by S.P. Timoshenko. The stress-strain state of elastic inhomogeneous isotropic shallow thin-walled shell constructions is studied. The stress-strain state of shell constructions is described by a system of the five equilibrium equations and by the five static boundary conditions with respect to generalized displacements. The aim of the work is to find generalized displacements from a system of equilibrium equations that satisfy given static boundary conditions. The research is based on integral representations for generalized displacements containing arbitrary holomorphic functions. Holomorphic functions are found so that the generalized displacements should satisfy five static boundary conditions. The integral representations constructed this way allow to obtain a nonlinear operator equation. The solvability of the nonlinear equation is established with the use of contraction mappings principle.

Generalized displacements and momenta formulations of an electromechanical plunger

This paper deals with four different derivations of the governing equations of a solenoid plunger with lumped-parameter. Energy-based modeling is employed with extended Hamilton's principle with independent generalized coordinates and generalized momenta in order to be applicable to composite Lagrange's equations. In the electromechanical models, displacements and charges are regarded to be generalized coordinates, mechanical momenta and flux linkages are the generalized momenta. The derived systems of differential equations are solved numerically with the Runge-Kutta method.

About a new approach to calculating spiral clamps

The bearing capacity of spiral clamps, which are mounted on wires (cables) for their tension, connection, repair, etc., is studied. The design of spiral clamps is formed from stretched spirals that are wound onto conductors with an interference fit, which makes it possible to obtain tensile connections practically inseparable. The general problem of the interaction of spiral clamps and overhead line conductor layers is formulated. Different asymptotic solutions are given for initial and boundary value problems, and the design parameters of spiral clamps are determined to provide their carrying capacity. A wire layer is represented by the energy approach as an equivalent anisotropic elastic cylindrical shell, and wire construction as a whole is considered as a system of cylindrical shells inserted each other and interacting by forces of pressure and friction. The equivalence of the elastic properties of the shell to the properties of the wire layer is established using energy averaging. The constitutive relations obtained using the Castigliano theorem relate the generalized displacements and the corresponding forces. The matrix in these ratios is a stiffness matrix or flexibility matrix of a spiral wire structure. Such approach allows variety of interaction problems for spiral clamps with conductor layers to be solved, and the force transfer mechanism to be investigated from common positions. Static equations are written from the equilibrium of the elementary shell ring. It is considered that the length of the clamp is so great that the mutual influence of its ends can be neglected; the clamp is modeled as semi-infinite shell. This model allows the different initial and boundary value problems to be formulated, depending on the boundary conditions and clamp mounting methods on a conductor.

An Elastic Interface Model for the Delamination of Bending-Extension Coupled Laminates

The paper addresses the problem of an interfacial crack in a multi-directional laminated beam with possible bending-extension coupling. A crack-tip element is considered as an assemblage of two sublaminates connected by an elastic-brittle interface of negligible thickness. Each sublaminate is modeled as an extensible, flexible, and shear-deformable laminated beam. The mathematical problem is reduced to a set of two differential equations in the interfacial stresses. Explicit expressions are derived for the internal forces, strain measures, and generalized displacements in the sublaminates. Then, the energy release rate and its Mode I and Mode II contributions are evaluated. As an example, the model is applied to the analysis of the double cantilever beam test with both symmetric and asymmetric laminated specimens.

Isogeometric boundary integral formulation for Reissner’s plate problems

Purpose This paper aims to develop a new isogeometric boundary element formulation based on non-uniform rational basis splines (NURBS) curves for solving Reissner’s shear-deformable plates. Design/methodology/approach The generalized displacements and tractions along the problem boundary are approximated as NURBS curves having the same rational B-spline basis functions used to describe the geometrical boundary of the problem. The source points positions are determined over the problem boundary by the well-known Greville abscissae definition. The singular integrals are accurately evaluated using the singularity subtraction technique. Findings Numerical examples are solved to demonstrate the validity and the accuracy of the developed formulation. Originality/value This formulation is considered to preserve the exact geometry of the problem and to reduce or cancel mesh generation time by using NURBS curves employed in computer aided designs as a tool for isogeometric analysis. The present formulation extends such curves to be implemented as a stress analysis tool.