In this paper one introduces a method of multiscale modelling called collection of dynamical systems with dimensional reduction. The method is suggested to be an appropriate approach to theoretical modelling of phenomena in mechanics of materials having in mind especially dynamics of processes. Within this method one formalizes scale of averaging of processes during modelling. To this end a collection of dynamical systems is distinguished within an elementary dynamical system. One introduces a
dimensional reduction procedure which is designed to be a method of transition between various scales. In order to consider continuum models as obtained by means of the dimensional reduction one introduces continuum with finite-dimensional fields. Owing to geometrical elements associated with the elementary dynamical system we can formalize scale of averaging within continuum mechanics approach. In general presented here approach is viewed as a continuation of the rational mechanics.
mechanics of materials; multiscale modelling.
Jaroslaw Kaczmarek: Institute of Fluid-Flow Machinery, Polish Academy of Sciences, 80-952 Gdansk, ul. J.Fiszera 14, Poland
Concrete is a heterogeneous material consisting of coarse aggregate, mortar matrix and interfacial zones at the meso level. Though studies have been done to interpret the fracture process in concrete using meso level models, not much work has been done for simulating the macroscopic behaviour of reinforced concrete structures using the meso level models. This paper presents a procedure for the mesoscopic analysis of reinforced concrete beams using a modified micro truss model. The micro truss model is derived based on the framework method and uses the lattice meshes for representing the coarse aggregate (CA), mortar matrix, interfacial zones and reinforcement bars. A simple procedure for generating a random aggregate structure is
developed using the constitutive model at meso level. The study reveals the potential of the mesoscopic numerical simulation using a modified micro truss model to predict the nonlinear response of reinforced concrete structures. The modified micro truss model correctly predicts the load-deflection behaviour, crack pattern and ultimate load of reinforced concrete beams failing under different failure modes.
mesoscopic analysis; micro truss; reinforced concrete; framework method.
Praveen Nagarajan: Department of Civil Engineering, National Institute of Technology Calicut, NIT Campus P.O., Calicut, Kerala 673601, India
U.B. Jayadeep: Department of Mechanical Engineering, National Institute of Technology Calicut, NIT Campus P.O., Calicut, Kerala 673601, India
T.M. Madhavan Pillai: Department of Civil Engineering, National Institute of Technology Calicut, NIT Campus P.O., Calicut, Kerala 673601, India
In this paper, a simple approach is presented for studying the dynamic response of multi-span steel bridges supported by pylons of different heights, subjected to earthquake motions acting along the axis of the bridge with spatial variations. The analysis is carried out using the modal analysis technique, while the solution of the integral-differential equations derived is obtained using the successive approximations technique. It was found that the height of piers and the quality of the foundation soil can
affect significantly the dynamical behavior of the bridges studied. Illustrative examples are presented to highlight the points of concern and useful conclusions are gathered.
bridge dynamics; piers; earthquakes; axial motion.
I.G. Raftoyiannis: Laboratory of Steel Structures, Department of Civil Engineering, National Technical University of Athens, 9 Iroon Polytechneiou St., Zografou Campus, Athens 15780, Greece
T.G. Konstantakopoulos: Laboratory of Steel Structures, Department of Civil Engineering, National Technical University of Athens, 9 Iroon Polytechneiou St., Zografou Campus, Athens 15780, Greece
G.T. Michaltsos: Laboratory of Steel Structures, Department of Civil Engineering, National Technical University of Athens, 9 Iroon Polytechneiou St., Zografou Campus, Athens 15780, Greece
The effect of soil-structure interaction on a single-storey, two-bay space frame resting on a pile group embedded in the cohesive soil (clay) with flexible cap is examined in this paper. For this purpose, a more rational approach is resorted to using the finite element analysis with realistic assumptions. Initially, a 3-D FEA is carried out independently for the frame on the premise of fixed
column bases in which members of the superstructure are discretized using the 20-node isoparametric continuum elements. Later, a model is worked out separately for the pile foundation, by using the beam elements, plate elements and spring elements to model the pile, pile cap and soil, respectively. The stiffness obtained for the foundation is used in the interaction analysis of the frame to quantify the effect of soil-structure interaction on the response of the superstructure. In the parametric study using the substructure approach (uncoupled analysis), the effects of pile spacing, pile configuration, and pile diameter of the pile group on the response of superstructure are evaluated. The responses of the superstructure considered include the displacement at top of the frame and moments in the columns. The effect of soilstructure interaction is found to be quite significant for the type of foundation considered in the study. Fair agreement is observed between the results obtained herein using the simplified models for the pile foundation and those existing in the literature based on a complete three dimensional analysis of the
building frame - pile foundation - soil system.
foundation; frame; piles; simplified models; soil-structure interaction; superstructure
H.S. Chore: Department of Civil Engineering, Datta Meghe College of Engineering, Sector-3, Airoli, Navi Mumbai- 400 708, India
R.K. Ingle: Department of Applied Mechanics, Visvesvaraya National Institute of Technology (VNIT), Nagpur- 440 010, India
V.A. Sawant: Department of Civil Engineering, Indian Institute of Technology (IIT), Roorkee - 247 667, India
The steady state response of a rotating generalized thermoelastic solid to a moving point load has been investigated. The transformed components of displacement, force stress and temperature distribution are obtained by using Fourier transformation. These components are then inverted and the results are obtained in the physical domain by applying a numerical inversion method. The numerical results are presented graphically for a particular model. A particular result is also deduced from the
rotation; generalized thermoelasticity; fourier transform; temperature distribution.
Praveen Ailawalia: Department of Mathematics, M.M. Engineering College, Maharishi Markandeshwar University,
Mullana District Ambala, Haryana, India
Naib Singh Narah: Department of Mathematics, D.A.V College, Ambala City, Haryana, India
In recent years, study of the static response of pavements to moving vehicle and aircraft loads has received significant attention because of its relevance to the design of pavements and airport runways. The static response of beams resting on an elastic foundation and subjected to moving loads was studied by several researchers in the past. However, most of these studies were limited to steady-state analytical solutions for infinitely long beams resting on Winkler-type elastic foundations. Although the modelling of subgrade as a continuum is more accurate, such an approach can hardly be incorporated in analysis due to its complexity. In contrast, the two-parameter foundation model provides a better way for simulating the underlying soil medium and is conceptually more appealing than the one-parameter
(Winkler) foundation model. The finite element method is one of the most suitable mathematical tools for analysing rigid pavements under moving loads. This paper presents an improved solution algorithm based on the finite element method for the static analysis of rigid pavements under moving vehicular or aircraft loads. The concrete pavement is discretized by finite and infinite beam elements, with the latter for modelling the infinity boundary conditions. The underlying soil medium is modelled by the Pasternak
model allowing the shear interaction to exist between the spring elements. This can be accomplished by connecting the spring elements to a layer of incompressible vertical elements that can deform in transverse shear only. The deformations and forces maintaining equilibrium in the shear layer are considered by assuming the shear layer to be isotropic. A parametric study is conducted to investigate the effect of the position of moving loads on the response of pavement.
beam element; damping; foundation; moving loads; pavement; Pasternak
V.A. Patil: Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee-247667, Uttarakhand, India
V.A. Sawant: Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee-247667, Uttarakhand, India
Kousik Deb: Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur-721302, India