Preface Bibliography 1. Interpolation. Introduction The Taylor expansion The finite Taylor series with the remainder term Interpolation by polynomials The remainder of Lagrangian interpolation formula Equidistant interpolation Local and global interpolation Interpolation by central differences Interpolation around the midpoint of the range The Laguerre polynomials Binomial expansions The decisive integral transform Binomial expansions of the hypergeometric type Recurrence relations The Laplace transform The Stirling expansion Operations with the Stirling functions An integral transform of the Fourier type Recurrence relations associated with the Stirling series Interpolation of the Fourier transform The general integral transform associated with the Stirling series Interpolation of the Bessel functions 2. Harmonic Analysis. Introduction The Fourier series for differentiable functions The remainder of the finite Fourier expansion Functions of higher differentiability An alternative method of estimation The Gibbs oscillations of the finite Fourier series The method of the Green's function Non-differentiable functions Dirac's delta function Smoothing of the Gibbs oscillations by Fejer's method The remainder of the arithmetic mean method Differentiation of the Fourier series The method of the sigma factors Local smoothing by integration Smoothing of the Gibbs oscillations by the sigma method Expansion of the delta function The triangular pulse Extension of the class of expandable functions Asymptotic relations for the sigma factors The method of trigonometric interpolation Error bounds for the trigonometric interpolation method Relation between equidistant trigonometric and polynomial interpolations The Fourier series in the curve fitting 3. Matrix Calculus. Introduction Rectangular matrices The basic rules of matrix calculus Principal axis transformation of a symmetric matrix Decomposition of a symmetric matrix Self-adjoint systems Arbitrary n x m systems Solvability of the general n x m system The fundamental decomposition theorem The natural inverse of a matrix General analysis of linear systems Error analysis of linear systems Classification of linear systems Solution of incomplete systems Over-determined systems The method of orthogonalisation The use of over-determined systems The method of successive orthogonalisation The bilinear identity Minimum property of the smallest eigenvalue 4. The Function Space. Introduction The viewpoint of pure and applied mathematics The language of geometry Metrical spaces of infinitely many dimensions The function as a vector The differential operator as a matrix The length of a vector The scalar product of two vectors The closeness of the algebraic approximation The adjoint operator The bilinear identity The extended Green's identity The adjoint boundary conditions Incomplete systems Over-determined systems Compatibility under inhomogeneous boundary conditions Green's identity in the realm of partial differential operators The fundamental field operations of vector analysis Solution of incomplete systems 5. The Green's Function. Introduction The role of the adjoint equation The role of Green's identity The delta function -- The existence of the Green's function Inhomogeneous boundary conditions The Green's vector Self-adjoint systems The calculus of variations The canonical equations of Hamilton The Hamiltonisation of partial operators The reciprocity theorem Self-adjoint problems Symmetry of the Green's function Reciprocity of the Green's vector The superposition principle of linear operators The Green's function in the realm of ordinary differential operators The change of boundary conditions The remainder of the Taylor series The remainder of the Lagrangian interpolation formula

Linear Differential Operators. By C. Lanczos. Pp. 580. 80s. 1961. (Van Nostrand, London)

Stress-strain curves for hot-rolled steels

Abstract This paper presents theoretical descriptions of the key phenomena that govern the behaviour of composite framed structures in fire. These descriptions have been developed in parallel with large scale computational work undertaken as a part of a research project (The DETR-PIT Project, Behaviour of steel framed structures under fire conditions) to model the full-scale fire tests on a composite steel framed structure at Cardington (UK). Behaviour of composite structures in fire has long been understood to be dominated by the effects of strength loss caused by thermal degradation, and that large deflections and runaway resulting from the action of imposed loading on a ‘weakened’ structure. Thus ‘strength’ and ‘loads’ are quite generally believed to be the key factors determining structural response (fundamentally no different from ambient behaviour). The new understanding produced from the aforementioned project is that, composite framed structures of the type tested at Cardington possess enormous reserves of strength through adopting large displacement configurations. Furthermore, it is the thermally induced forces and displacements, and not material degradation that govern the structural response in fire. Degradation (such as steel yielding and buckling) can even be helpful in developing the large displacement load carrying modes safely. This, of course, is only true until just before failure when material degradation and loads begin to dominate the behaviour once again. However, because no clear failures of composite structures such as the Cardington frame have been seen, it is not clear how far these structures are from failure in a given fire. This paper attempts to lay down some of the most important and fundamental principles that govern the behaviour of composite frame structures in fire in a simple and comprehensible manner. This is based upon the analysis of the response of single structural elements under a combination of thermal actions and end restraints representing the surrounding structure.

Fundamental principles of structural behaviour under thermal effects (large composite buildings under compartment fires)

Design Of Steel Structures

Description of stress-strain curves for cold-formed steels

Solid or shell finite elements to model thick cylindrical tubes and shells under global bending

Nonlinear stability of thin elastic cylinders of different length under global bending

Statistical analysis of the material properties of selected structural carbon steels

The global growth in wind energy suggests that wind farms will increasingly be deployed in seismically active regions, with large arrays of similarly designed structures potentially at risk of simultaneous failure under a major earthquake. Wind turbine support towers are often constructed as thin-walled metal shell structures, well known for their imperfection sensitivity, and are susceptible to sudden buckling failure under compressive axial loading.

This study presents a comprehensive analysis of the seismic response of a 1.5-MW wind turbine steel support tower modelled as a near-cylindrical shell structure with realistic axisymmetric weld depression imperfections. A selection of 20 representative earthquake ground motion records, 10 ‘near-fault’ and 10 ‘far-field’, was applied and the aggregate seismic response explored using lateral drifts and total plastic energy dissipation during the earthquake as structural demand parameters.

The tower was found to exhibit high stiffness, although global collapse may occur soon after the elastic limit is exceeded through the development of a highly unstable plastic hinge under seismic excitations. Realistic imperfections were found to have a significant effect on the intensities of ground accelerations at which damage initiates and on the failure location, but only a small effect on the vibration properties and the response prior to damage. Including vertical accelerations similarly had a limited effect on the elastic response, but potentially shifts the location of the plastic hinge to a more slender and, therefore, weaker part of the tower. The aggregate response was found to be significantly more damaging under near-fault earthquakes with pulse-like effects and large vertical accelerations than far-field earthquakes without these aspects.

/pdf/seismic-analysis-of-a-tall-metal-wind-turbine-support-tower-1qpkjwivg6.pdf

Seismic analysis of a tall metal wind turbine support tower with realistic geometric imperfections

https://www.tpbin.com/Uploads/Subjects/b70dd1a2-b1ae-4f39-a8bf-32e266657138.pdf

Adam J. Sadowski

Papers

Solid or shell finite elements to model thick cylindrical tubes and shells under global bending

Nonlinear stability of thin elastic cylinders of different length under global bending

Statistical analysis of the material properties of selected structural carbon steels

Seismic analysis of a tall metal wind turbine support tower with realistic geometric imperfections

Buckling of very slender metal silos under eccentric discharge