Elastic Bed Research Articles

Prediction of shallow-foundation settlements and selection of bed models for slab analysis

A brief review is given for the development of methods of analyzing slabs on an elastic bed (from N. M. Gersevanov to the present) with the isolation of problems relative to bed models. A method of settlement calculation is described on the basis of layer-by-layer summation with consideration of the structural strength of the soil and the slab suitable for use in the analysis.

Gersevanov’s functional interrupters and analysis of structures on elastic beds

Gersevanov’s functional interrupters and analysis of structures on elastic beds

VIBRATIONS OF CIRCULAR CYLINDRICAL SHELLS WITH NONUNIFORM CONSTRAINTS, ELASTIC BED AND ADDED MASS; PART I: EMPTY AND FLUID-FILLED SHELLS

Circular cylindrical shells with non uniform edge constraints (with zero radial and circumferential displacement) are investigated, including riveted shells. The linear modes of simply supported shells vibrating in vacuo are used as admissible functions, and the solution is obtained with the artificial spring method. The Flügge theory of shells is used and in-plane inertia is retained. Any shell constraint other than simple supports can be studied with the proposed method. Complicating effects due to the contained inviscid fluid, elastic bed of partial axial and angular dimensions, intermediate constraints and added mass are considered. The convergence of the method is numerically investigated and the effect of the number of rivets (clamped arcs) on shell modes is studied.

Analysis of slabs partially supported on an elastic bed

This paper addresses problems of the bending of infinite and semi-infiniteslabs on an elastic bed where support is lacking in individual sections in the form of trenches situated parallel to the coordinate axes of the surface of the slab. Precise analytical solutions of the problems are obtained by the method of generalized solutions. Numerical results are obtained and analyzed.

Well-Posedness of Mixed Formulations in Elasticity

Mixed formulations in elasticity are analysed and existence and uniqueness of the solution are discussed in the context of Hilbert space theory. New results, referred to in the analysis of elasticity problems, are proved. They are concerned with the closedness of the product of two linear operators and a projection property equivalent to the closedness of the sum of two closed, subspaces. A set of two necessary and sufficient conditions for the well-posedness of an elastic problem with a singular elastic compliance procides the most general result of this kind in linear elasticity. Sufficient criteria for the well-posedness of elastic problems in structural mechanics including the presence of supporting elastic beds are contributed and applications are exemplified.

Well-Posedness of Mixed Formulations in Elasticity

Mixed formulations in elasticity are analysed and existence and uniqueness of the solution are discussed in the context of Hilbert space theory. New results, referred to in the analysis of elasticity problems, are proved. They are concerned with the closedness of the product of two linear operators and a projection property equivalent to the closedness of the sum of two closed subspaces. A set of two necessary and sufficient conditions for the well-posedness of an elastic problem with a singular elastic compliance provides the most general result of this kind in linear elasticity. Sufficient criteria for the well-posedness of elastic problems in structural mechanics including the presence of supporting elastic beds are contributed and applications are exemplified.

A theoretical tire model based on the general field equations

Most of the models for the structure-borne sound behavior of tires are designed for the low-frequency range (i.e., below 300–400 Hz) and often contain the geometrical details of the tire. Above this frequency range the curvature of the tire can be omitted while the internal structure (i.e., multilayers of steel and rubber) increases in importance. For this higher-frequency range, a model has been developed based on the general field equations. The model consists of a double-layered thick plate, representing the tire belt, which is prestressed due to the internal pressure in the tire. An elastic bedding supports the plate, in order to take into account the compression of the air inside the tire cavity and also to take into account the influence of the side walls on the belt. Both the radial and the tangential motions in the belt are included, since the model is based on the general field equations. The model also incorporates the effect of the local deformation of the soft rubber surface. Results from the model are compared with results from other models from the literature and with measurements.

Mechanical significance of ammonoid septa with complex sutures

Pre- and post-19th century hypotheses relating hydrostatic pressure to the mechanical function of sutural complexity are compared. The old ideas gave rise to the 19th century ‘Buckland hypothesis’, which is in turn largely synonymous with the ‘Westermann model’. Buckland (1836) postulated that fluted septa buttressed the weak flanks of the phragmocone wall. Two new parameters are introduced to define the covariation between the strength of cylindrical segments of the wall flank bounded by the distance between adjacent lobe and saddle-flutes in transverse sections. The product of the index of wall strength (IWS) and this inverse support angle (ISA) predicts the buckling pressure in a cylinder of infinite length, and it implies that coiled nautiloids were more likely to be imploded via their whorl flanks than the apparently weaker oxyconic ammonoids. The widely used index of sutural complexity (ISC) measures the marginal corrugation which obscures this trend and acts as an elastic bed for both strong and weak walls. However, the ISC is more proportional to habitat depth than the buckling pressure when all other factors are constant. The central thickness of each fluted septum was increased in direct proportion to the distance spanned by the septum and the hydrostatic pressure on it in the ‘last septum’ position. The marginal thickness was maintained at a more constant value, which permitted the suture to increasingly act like a spring or shock absorber, as the wall thickness was enlarged during ontogeny. Both the ratios, between the central and marginal thicknesses and the closely related ISC, therefore, increased with shell diameter and habitat depth.

Free Vibrations of Cylindrical Shells with Non-Axisymmetric Mass Distribution on Elastic Bed

The free vibrations of circular cylindrical shells partiallyloaded by a distributed mass and rested on an elastic bed are studied in this paper. Both the mass-load and the elastic bed are assumed to be applied on limited arcs and with arbitrary distributions in circumferential direction,while they are considered to be uniformly distributed in longitudinaldirection on the entire shell length. Therefore, the problem is notaxisymmetric. The solution is obtained by using the development of theflexural mode shapes in a Fourier series, whose coefficients are determinedby rendering the Rayleigh quotient stationary, so a Galerkin equation isobtained. The proposed method is independent of the boundary conditionsat the shell ends. The results are satisfactorily compared to FEM results.Finally, the influence of the mass-load and of the bed stiffness on thenatural frequencies and mode shapes of a simply supported shell is shownand discussed.

Bending of a rectangular plate supported on an elastic winkler bed with allowance for longitudinal forces

The problem of the bending of a rectangular slab lying on an elastic Winkler bed with allowance for longitudinal forces applied in the median plane under an arbitrary loading is discussed. A method for solution of problems involving the design of structures on a deformed bed, which consists in the fact that the structure's equilibrium equation assigned to a finite region is extended over the entire region using generalized functions, is used. This makes it possible to use integral equations with simple kernels for its solution.

Mass transport in water waves over an elastic bed

The mass transport velocity in water waves propagating over an elastic bed is investigated. Water is assumed to be incompressible and slightly viscous. The elastic bed is also incompressible and satisfies the Hooke’s law. For a small amplitude progressive wave perturbation solutions via a boundary-layer approach are obtained. Because the wave amplitude is usually larger than the viscous boundary layer thickness and because the free surface and the interface between water and the elastic bed are moving, an orthogonal curvilinear coordinate system (Longuet-Higgins 1953) is used in the analysis of free surface and interfacial boundary layers so that boundary conditions can be applied on the actual moving surfaces. Analytical solutions for the mass transport velocity inside the boundary layer adjacent to the elastic seabed and in the core region of the water column are obtained. The mass transport velocity above a soft elastic bed could be twice of that over a rigid bed in the shallow water.

General model for the approximate calculation of elastic-bed settlements

A model for the approximate calculation of elastic beds, which is based on the concept of pressure-distribution angle, is proposed. The model can be used for an elastic half plane, half space, and a layer of finite thickness. In the latter case, the computational scheme reduces to a Winkler model, if the distribution angle is a right angle. It is pointed out that the settlement coefficients computed for an elastic half space and layer of finite thickness differ by only a small constant value.

Design of flexible slabs of arbitary planform on any type of elastic bed : S. V. Bosakov, Soil Mechanics & Foundation Engineering, 31(1), 1994, p 8

Design of flexible slabs of arbitary planform on any type of elastic bed : S. V. Bosakov, Soil Mechanics & Foundation Engineering, 31(1), 1994, p 8

Nonlinear parametric oscillation of a beam contacting with ideal compressible liquid in a channel

The influence of compressible liquid on nonlinear oscillation of a channel back boundary is studied. The back boundary is a beam with a thrust on an elastic bed. The beam is excited by parametric longitudinal compressing forces. Using the Galerkin procedure the starting equation takes the form: Ẅ1+a(t)W1+εẆ1=bW31+cW1W22=0, Ẅ2+f(t)W2+γW32+gW2W21=0. The fundamental resonances of the beam are examined by using the multiple-scales averaging analysis. The presence of liquid leads to reduction of the range where stable oscillation of the system is possible. Numerical simulation of the process in the phase space has been conducted and chaotic behavior of the system has been found. Precision algorithms of Runge-Kutta (DOPRI) have been used for the numerical simulation. The numerical simulations are studied in the context of Runge-Kutta simplex methods. Qualitative analysis of process dynamics has been obtained. Lyapunov exponents and fractal dimensionality have been determined; they prove the presence of a strange attractor in the system.

Design of flexible slabs of arbitrary planform on any type of elastic bed

Design of flexible slabs of arbitrary planform on any type of elastic bed

Models of layer deformation of an elastic half space

Applied modes of the deformation of an inhomogeneous elastic bed consisting of a layer of finite thickness and a semi-infinite space, the elastic constants of which differ markedly, are proposed. An explicit form of the equations describing the theory of deformation is established. An evaluation of the error of the resultant equations is made, and the range of their application determined.

Deformation of orthotropic noncircular cylindrical shells in an elastic bed

Deformation of orthotropic noncircular cylindrical shells in an elastic bed

Stress transfer and seismic instabilities in the upper crust: example of the western Pyrenees

When the regional state of stress is close to the condition for earthquakes to occur, small stress and strain changes could trigger seismic instabilities. Stress diffusion ( Δσ = 1–2 MPa) has been suggested to explain, at lithospheric scale, space and time correlated earthquakes and surface deformations in subduction zones (100–200 km, 10–40 years). We test the possible regional mechanisms, at the upper crustal scale, in the western Pyrenees, where major regional events (M max = 5.7), locally induced events and subsurface fluid pressure fluctuations are temporally and spatially correlated. In a first phase, fluid withdrawal (decrease of pore pressure of the aquifer at the gas-water interface) affects the natural regional seismicity rate. The locked fault inhibits small events for a time, during which tectonic stresses accumulate. Major regional events then occur on the Pyrenean Fault, when the energy of deformation is large enough to allow seismic instabilities to occur. These major events (M 1 > 5) trigger seismic instabilities (M 1 = 4), in the vicinity of the gas extraction area, 30 km away. As a result of gas extraction, the Lacq field zone has local weakness characteristics similar to the neighbouring main active fault. The Pyrenean earthquakes lead the gas field events by 2 years. This correlation is consistent with a viscoelastic model, where salt rock acts as a viscoelastic channel, below an elastic bed. The possible connections proposed here may give a new insight worldwide in understanding the role of fluids in seismic instabilities and seismic risk assessment in the neighbouring of man-made fluid pressure fluctuations, when natural seismic activity is high.

Calculation of the stress state of a slab on an inhomogeneous elastic bed

Calculation of the stress state of a slab on an inhomogeneous elastic bed

Refinement of methods for calculating beams on an elastic bed

Refinement of methods for calculating beams on an elastic bed