Johan Blaauwendraad

Spectral element technique for efficient parameter identification of layered media. I. Forward calculation

Abstract This contribution deals with the use of spectral analysis as a means of analysing the dynamic behaviour of the axially symmetric multi-layered systems as a result of a transient force. The objective of this research work is to develop an accurate and computationally efficient forward tool suitable for solving inverse problems. The spectral element technique is utilized. Details of the mathematical derivation, implementation and verification of newly developed axi-symmetric and half-space spectral elements are presented. It is shown that the suitability of the spectral element method to such a problem encompasses in its ability to model a whole layer without the need for subdivisions. As a consequence, the size of the modelled structure becomes as large as the number of the layers involved. This reduces the computational requirements substantially and hence enables efficient utilization of the method in iterative algorithms for solving inverse problems.

Spectral element technique for efficient parameter identification of layered media: Part II: Inverse calculation

Abstract In Part I of this series of articles a forward model was presented for the simulation of wave propagation in a multi-layer system by means of the spectral element method. In the current article and, on the basis of the forward model, a procedure is presented for inverse calculation of the system parameters. The proposed procedure is based on iterative comparisons of measured versus theoretically determined system transfer functions. The performance of three minimization algorithms; factored Secant update, modified Levenberg–Marquardt and Powell hybrid for solving the resulting system of nonlinear equations is evaluated. For the problem under consideration, the Powell hybrid algorithm exhibits better stability and convergence characteristics. As an application, the inverse procedure is utilized for the determination of pavement layer moduli and thicknesses via the use of the falling weight deflectometer (FWD) test. The calculations show that the developed procedure is accurate and computationally efficient. As a result of these calculations, modifications to the standard practice of FWD measurements and instrumentation are suggested.

Stringer Panel Model for Structural Concrete Design

A large number of concrete structures can be treated as two-dimensional plate problems. Both the load and the support reactions have lines of action that coincide with the plane of the structure. This is how beams, walls, dapped beams, corbels, etc., are analyzed. In practical design, two prominent methods of analysis exist: the strutand-tie method and the finite element method. First, we will briefly discuss the advantages and disadvantages of these two methods, and subsequently introduce a new method called the stringer panel model for the design of economic and rational reinforcement. This approach takes into account both equilibrium and compatibility and has the advantage of being highly design-oriented. An additional advantage of this method is that an estimation of the crack width in the serviceability limit state is part of the result.

Spectral element technique for efficient parameter identification of layered media. Part III: viscoelastic aspects

This article addresses the issues of wave propagation in elastic–viscoelastic layered systems and viscous parameter identification from non-destructive dynamic tests. A methodology that combines the spectral element technique, for the simulation of wave propagation, with the differential operator technique, for stress–strain relationship in viscoelastic materials, is adopted. The compatibility between the two techniques stems from the fact that both can be treated in the frequency domain, which enables naturally the adoption of Fourier superposition. The mathematical formulation of spectral elements for Burger’s viscoelastic material model is highlighted. Also, an inverse procedure for the identification of the material’s Young’s moduli and complex moduli for layer systems is described. It is shown that the proposed methodology enables the substitution of an expensive laboratory testing procedure for the determination of material complex moduli with non-destructive dynamic testing. 2002 Elsevier Science Ltd. All rights reserved.

Poroelastic spectral element for wave propagation and parameter identification in multi-layer systems

Abstract This contribution deals with the use of Biots theory of propagation of elastic waves in a fluid-saturated porous solid in conjunction with the computationally efficient spectral element technique as a means for forward analysis of the dynamic behavior of multi-layer systems consisting of both one- and two-phase material layers. Details of the mathematical formulation and verification of an axi-symmetric semi-infinite spectral element for a fully saturated porous medium are presented. The spatial domain of the element in the vertical direction is assumed to extend to infinity. In the radial direction it extends to a finite distance. In the last part of this contribution an example is presented of the use of the developed element for parameter identification of pavement layers via the use of falling weight deflectometer test.

Experimental Calibration Of A Viscoplastic-Fracturing Computational Model

An extensive experimental and analytical investigation is currently being carried out on the mechanisms leading to the initiation and propagation of damage in viscoplastic materials. One of the major goals of the investigation is the development and the finite elements implementation of a generalised triaxial, strain rate sensitive, history and temperature dependent constitutive model. Explicit procedures have been formulated for the experimental determination of the model parameters. As a minimum, only uniaxial test results are needed for determination of the basic parameters. The model has been implemented in the finite element code CAPA-3D. Results of the utilization of CAPA-3D for the investigation of the dynamic non-linear response of a road pavement are reviewed in the last part of this contribution.

Quadrilateral shear panel

Abstract Various models of structures and structural elements use an assembly of stringers and shear panels. The normal forces in the stringers can vary linearly and the membrane panels have constant shear. Often, these shear panels can be just rectangular but sometimes shear panels with a non-rectangular shape need to be used. In this paper a mathematical formulation is presented for a linear–elastic shear panel with a quadrilateral shape. The panel stiffness matrix is derived by the discrete element method, which yields a simple and efficient computational formulation. Comparison with finite element computations shows that the stiffness matrix is sufficiently accurate for engineering design.

Console with Opening

The subject of this chapter is a console with opening under a point load. The square console is supported at the right-hand vertical edge and loaded on top of the free left-hand edge. The square opening at the centre of the console obstructs the transfer of the load to the supported edge. Therefore, the exercise is transformed into a free square wall with opening under two equilibrating compressive diagonal loads, one at the top left-hand corner and one at the bottom right-hand corner. The coarsest stringer-panel model possible has just one panel each above, below, to the left and to the right of the opening. These four panels have an aspect ratio of 2. Due to indeterminacy, many equilibrium states are possible, of which two are presented. The first SPM solution is in close agreement with the stresses and trajectories from a finite element analysis. As expected, zero-force SPM members occur near the two load-free corners. Two corresponding strut-and-tie models are depicted. The second SPM solution deviates substantially from the stresses and trajectories obtained from FEA: large member forces occur near the load-free corners, which will require substantial redistribution of stresses. This also holds true for the two corresponding strut-and-tie models derived from the second SPM solution.

Diaphragm Floor Slab

The subject of the final chapter is the analysis of a floor slab acting as a diaphragm in a multi-storey building to resist horizontal seismic loading. The floor length is 56.00 m and the width 22.60 m. The seismic load is active in the shorter floor direction and is resisted by two reinforced concrete cores, with side lengths about 7.00 m, and by 22 concrete columns. The cores and springs are all modelled as springs. The seismic loading is based on an earthquake with a strength of 0.42 times the acceleration of gravity. The floor mass is multiplied by this seismic acceleration, yielding a uniformly distributed area load. The analysis is performed using the Matlab code given in Appendix B. For modelling of the springer-panel model, SAP2000 is applied. At the chosen spring stiffnesses, 16% of the seismic loading is resisted by the columns and 84% by the cores.

Introduction to Stringer-Panel Models

The stringer-panel model (SPM) is intended as companion method to the better-known strut-and-tie model (STM) for the design of D-regions where Bernoulli beam theory does not apply. To explain the merits of the SPM, first an overview of the STM is presented, setting out its design steps and challenges. The SPM applies two different elements: stringers to carry normal forces, and panels for the transmission of uniform shear membrane forces. The SPM has its roots in two different disciplines: on the one hand structural concrete plasticity, and on the other linear-elastic analysis of redundant aeroplane structures. The SPM can be used in such various fields as seismic design and performance-based design. The focus of the book is on building the model and determining the forces in stringers and panels. For simple models, analysis by hand will suffice. For more complicated models, two programs on the Internet are freely accessible.