D.E. Beskos

Boundary Element Methods in Dynamic Analysis

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BENDING AND STABILITY ANALYSIS OF GRADIENT ELASTIC BEAMS

Abstract The problems of bending and stability of Bernoulli–Euler beams are solved analytically on the basis of a simple linear theory of gradient elasticity with surface energy. The governing equations of equilibrium are obtained by both a combination of the basic equations and a variational statement. The additional boundary conditions are obtained by both variational and weighted residual approaches. Two boundary value problems (one for bending and one for stability) are solved and the gradient elasticity effect on the beam bending response and its critical (buckling) load is assessed for both cases. It is found that beam deflections decrease and buckling load increases for increasing values of the gradient coefficient, while the surface energy effect is small and insignificant for bending and buckling, respectively.

Static, seismic and stability analyses of a prototype wind turbine steel tower

Selected results of a study concerning the load bearing capacity and the seismic behavior of a prototype steel tower for a 450 kW wind turbine with a horizontal power transmission axle are presented. The main load bearing structure of the steel tower rises to almost 38 m high and consists of thin-wall cylindrical and conical parts, of varying diameters and wall thicknesses, which are linked together by bolted circular rings. The behavior and the load capacity of the structure have been studied with the aid of a refined finite element and other simplified models recommended by appropriate building codes. The structure is analyzed for static and seismic loads representing the effects of gravity, the operational and survival aerodynamic conditions, and possible site-dependent seismic motions. Comparative studies have been performed on the results of the above analyses and some useful conclusions are drawn pertaining to the effectiveness and accuracy of the various models used in this work.

Boundary element methods in mechanics

1. Introduction to Boundary Element Methods (D.E. Beskos). 2. Potential Theory (D.E. Beskos). 3. Elastostatics (M.S. Gomez-Lera, E. Alarcon). 4. Elastodynamics (S. Kobayashi). 5. Advanced Elastodynamic Analysis (P.K. Banerjee, S. Ahmad, G.D. Manolis). 6. Nonlinear Solid Mechanics (S. Mukherjee, A. Chandra). 7. Fracture Mechanics (T.A. Cruse). 8. Fluid Mechanics (J.A. Liggett). 9. Acoustics (R.P. Shaw). 10. Heat Conduction, Thermoelasticity and Consolidation (S. Sharp, S.L. Crouch). 11. Dynamic Soil-Structure Interaction (D.L. Karabalis, D.E. Beskos). 12. Fluid-Structure Interaction (C.A. Brebbia, J.C.F. Telles). Index.

Vibration isolation using open or filled trenches

The problem of structural isolation from ground transmitted vibrations by open or infilled trenches under conditions of plane strain is numerically studied. The soil medium is assumed to be linear elastic or viscoelastic, homogeneous and isotropic. Horizontally propagating Rayleigh waves or waves generated by the motion of a rigid foundation or by surface blasting are considered in this work. The formulation and solution of the problem is accomplished by the boundary element method in the frequency domain for harmonic disturbances or in conjunction with Laplace transform for transient disturbances. The proposed method, which requires a discretisation of only the trench perimeter, the soil-foundation interface and some portion of the free soil surface on either side of the trench appears to be better than either finite element or finite difference techniques. Some parametric studies are also conducted to assess the importance of the various geometrical, material and dynamic input parameters and provide useful guidelines to the design engineer.

3-D seismic response analysis of long lined tunnels in half-space

The dynamic response of infinitely long lined tunnels with a uniform cross-section buried into an elastic or viscoelastic half-space to body and surface harmonic seismic waves is numerically determined by a special direct boundary element method in the frequency domain. The waves have an arbitrary direction of propagation with respect to the axis of the tunnel and this renders the problem three-dimensional. However, this problem is effectively reduced to a two-dimensional one by a coordinate transformation and appropriate integration of the full-space dynamic fundamental solution along the direction of the tunnel axis. Quadratic isoparametric boundary line elements and advanced numerical integration techniques for the treatment of singular integrals produce results of high accuracy. Numerical results are presented for the case of an infinitely long lined tunnel of circular cross-section and compared against those of a full three-dimensional boundary element analysis, as well as those of other methods. Thus the proposed method is illustrated and its merits demonstrated.

Modelling of pile wave barriers by effective trenches and their screening effectiveness

Abstract The three-dimensional problem of isolation of vibration by a row of piles is studied numerically on the basis of a model replacing the row of piles by an effective trench in order to reduce the modelling complexity. The analysis is accomplished with the aid of an advanced frequency domain boundary element method, which is used for both the infilled trench and the soil medium in conjunction with a coupling procedure based on enforcement of equilibrium and compatibility at the trench–soil interface. Linear elastic or viscoelastic material behaviour is assumed for both the piles and the soil. The piles can be tubular or solid and have circular or square cross-section. The vibration source is a vertical force, harmonically varying with time, and the row of piles acts as a passive wave barrier. The effective trench model is constructed by invoking well known homogenization techniques used in the mechanics of fibre-reinforced composite materials, and its accuracy is compared against a rigorous boundary element analysis modelling each pile separately in full contact with the soil medium. On the basis of the effective trench model, the screening effectiveness of a row of piles is studied through parametric studies.

Vibration isolation using open or filled trenches Part 2: 3-D homogeneous soil

The isolation of structures from ground transmitted waves by open and infilled trenches in a three-dimensional context is numerically studied. The soil medium is assumed to be elastic or viscoelastic, homogeneous and isotropic. Waves generated by the harmonic motion of a surface rigid machine foundation are considered in this work. The formulation and solution of the problem is accomplished by the boundary element method in the frequency domain. The infinite space fundamental solution is used requiring discretization of the trench surface, the soil-foundation interface and some portion of the free soil surface. The proposed methodology is first tested for accuracy by solving three characteristic wave propagation problems with known solutions and then applied to several vibration isolation problems involving open and concrete infilled trenches. Three-dimensional graphic displays of the surface displacement pattern around the trenches are also presented.

Thermally induced vibrations of beam structures

A general numerical method is developed for determining the dynamic response of beam structures to rapidly applied thermal loads. The method consists of formulating and solving the dynamic problem in the Laplace transform domain with the aid of dynamic stiffness influence coefficients defined for a beam element in that domain and of obtaining the response by a numerical inversion of the transformed solution. Thus, the solution of the associated heat conduction problem, usually obtained by Laplace transform and needed for the computation of the thermal load, can be used in its transformed form. The effects of damping and of axial compressive forces on the structural response are also studied. Three examples are presented in detail to illustrate the proposed method and demonstrate its advantages.

Static, dynamic and stability analysis of structures composed of tapered beams

Abstract A new numerical method is proposed for the static, dynamic and stability analysis of linear elastic plane structures consisting of beams with constant width and variable depth. It is a finite element method based on an exact flexural and axial stiffness matrix and approximate consistent mass and geometric stiffness matrices for a linearly tapered beam element with constant width. Use of this method provides the exact solution of the static problem with just one element per member of a structure with linearly tapered beams and excellent approximate solutions of the dynamic and stability problems with very few elements per member of the structure in a computationally very efficient way. Very detailed comparison studies of the proposed method against a number of other known finite element methods with respect to accuracy and computational efficiency for cantilever tapered beams of rectangular and I cross section clearly favor the proposed method. A continuous beam, a gable frame and a portal frame consisting of tapered members are analyzed by the proposed method as well as by other known methods to illustrate the use of the method to structures composed of tapered beams.