Publisher Summary To calculate the vibrations of an embedded foundation, this chapter addresses t... more Publisher Summary To calculate the vibrations of an embedded foundation, this chapter addresses the wave mechanism generated at a material discontinuity corresponding to an interface between two layers. When the incident wave propagating in the initial cone encounters the discontinuity, a reflected wave and a refracted wave, each propagating in its own cone, are created. Enforcement of compatibility of displacement and equilibrium of the interface permits the reflected and refracted waves to be expressed as functions of the incident wave. The reflection coefficient, defined as the ratio of the reflected wave to the incident wave, depends on the properties of the two materials present at the interface and the frequency of the wave. The chapter calculates the reflection coefficient for the translational cone and the rotational cone. The derivations are performed for harmonic excitation. The chapter determines the dynamic-stiffness coefficients of a circular foundation on the surface of a layer overlying a flexible half-space for illustration, examines a disk embedded in a homogeneous half-space, discusses the representation of the problem for analysis by a computer program, and describes an efficient recursive implementation of such a program, including MATLAB listings of the key functions.
Publisher Summary This chapter explains the model of initial cone with outward wave propagation i... more Publisher Summary This chapter explains the model of initial cone with outward wave propagation in vibration analysis. The chapter is limited to those relationships that are required to calculate the dynamic-stiffness coefficients and the effective foundation input motion. As the analysis is performed in the frequency domain, the derivation is also performed for harmonic excitation in the elastic medium. The first of the two building blocks used to calculate the vibrations of an embedded foundation consists of a disk embedded in a layered half-space, modeled as a double cone, with each cone exhibiting outward wave propagation. Such a model is shown in the chapter for the vertical degree of freedom. As a special case, the disk is placed on the surface of the half-space that leads to a one-sided cone model. The chapter discusses the translational one-sided cone. The hypotheses and construction of the one-dimensional strength-of-materials approach using a tapered bar with the cross-section increasing in the direction of wave propagation—as in a cone—is addressed. The chapter derives the analogous relationships for the rotational one-sided cone and addresses the modifications necessary for the vertical and rocking degrees of freedom when Poisson's ratio approaches 1/2 yielding an infinite dilatational-wave velocity. The chapter presents the dynamic-stiffness coefficients of a (circular) foundation on the surface of a homogeneous half space that are compared with the results of a rigorous analysis.
Computational Fluid and Solid Mechanics 2003, Vols 1 and 2, Proceedings, 2003
Publisher Summary In this chapter, a novel semianalytical approach to continuum mechanics, known ... more Publisher Summary In this chapter, a novel semianalytical approach to continuum mechanics, known as the “scaled-boundary finite-element” method, is introduced for elasto-static problems involving an unbounded axisymmetric domain subjected to general loading. The accuracy and efficiency of the scaled boundary finite-element solutions are examined in the chapter by comparison with analytical solutions for a rigid circular footing on the surface of a homogeneous half-space subjected to vertical, horizontal, moment, and torsion loading. It is shown that as the number of nodes used to discretize the boundary increases, the computed solutions converge to the analytical solutions rapidly. Using a boundary discretized with 61 nodes, the discrepancies between the scaled-boundary finite-element solutions and the analytical solutions are negligible for all load cases.
Many researchers have studied traffic-induced ground vibrations. It was found that traffic-induce... more Many researchers have studied traffic-induced ground vibrations. It was found that traffic-induced ground vibration might disturb occupants in nearby structures, often impede normal operation of sensitive equipment, and under extreme cases, might cause architectural damages in structures. Many codes and standard organizations specify allowable ground vibration levels in terms of peak ground acceleration (PGA) and/or peak particle velocity (PPV), or peak ground vibrations together with principal ground vibration frequency (PF) to limit vibration effects on structures, human and sensitive equipment. Many empirical ground motion attenuation relations were derived from field measurement. Since wave propagation is highly site dependent, these empirical relations obtained by different researchers on different sites could differ significantly. In this paper, dynamic responses of four structural models, namely a low-rise residential structure, an office building, a medium-rise building and a high-rise building to field measured traffic-induced ground vibrations are calculated. The largest dynamic structural response time history in each structural model is extracted. The floor level that the largest dynamic response occurs is identified. The peak acceleration and peak velocity response spectrum of each structural model are estimated and compared with the allowable vibration limits for structure damage, for human perception or disturbance and for sensitive equipment. It is found that traffic-induced ground vibration is not strong enough to cause damage to RC structures, but might disturb occupants in structures near a busy road, and is strong enough to cause malfunctioning of sensitive equipment. Therefore, proper isolation is needed for sensitive equipment housed in structures near roads.
The scaled boundary method is a semi-analytical method developed by Wolf and Song (1996) to deriv... more The scaled boundary method is a semi-analytical method developed by Wolf and Song (1996) to derive the dynamic stiffness matrices of unbounded domains. A virtual work derivation for elastostatics developed by Deeks and Wolf (2002) improved the accessibility of the method by reformulating the complicated mathematics of the original derivation.
The 70th anniversary of the International Association of Universities provides an opportunity to ... more The 70th anniversary of the International Association of Universities provides an opportunity to look back over the post-World War II era, and to reflect on the drivers that have led to the international higher education environment we experience today. The anniversary also provides an opportunity to look forward and to consider how such a globalised system of universities might contribute to future society.
Journal of Zhejiang University Science a Applied Physics Engineering, Mar 1, 2012
ABSTRACT Hollow core slabs are becoming of increasing interest as the construction industry attem... more ABSTRACT Hollow core slabs are becoming of increasing interest as the construction industry attempts to minimise the impact of its activities on the environment. By forming voids in the interior of a concrete slab, the amount of concrete used can be reduced without significantly altering the capacity of the structure. In this study, we examined the inner force transfer mechanism of a column-supported cast-in-situ hollow core slab using finite element analysis. Both a hollow core slab and the corresponding solid slab were analysed using ANSYS and the results were compared. The orientation of the tube fillers causes the stiffness of the hollow slab to be orthotropic, potentially changing the distribution of load carried in the two orthogonal directions. Both the cross-section’s moments in the column strip and near the columns in the hollow core slab become larger than that in the solid floor. As well, the cross-section’s stiffness along the tube arrangement direction is larger than that of the radial cross-section, which causes the direction along the hole of the hollow core slab to carry more moment than the radial direction. The conversion factors of the two directions are proposed from the comparison for four typical areas of the hollow core slab, as are the moment distribution coefficients.
Publisher Summary To calculate the vibrations of an embedded foundation, this chapter addresses t... more Publisher Summary To calculate the vibrations of an embedded foundation, this chapter addresses the wave mechanism generated at a material discontinuity corresponding to an interface between two layers. When the incident wave propagating in the initial cone encounters the discontinuity, a reflected wave and a refracted wave, each propagating in its own cone, are created. Enforcement of compatibility of displacement and equilibrium of the interface permits the reflected and refracted waves to be expressed as functions of the incident wave. The reflection coefficient, defined as the ratio of the reflected wave to the incident wave, depends on the properties of the two materials present at the interface and the frequency of the wave. The chapter calculates the reflection coefficient for the translational cone and the rotational cone. The derivations are performed for harmonic excitation. The chapter determines the dynamic-stiffness coefficients of a circular foundation on the surface of a layer overlying a flexible half-space for illustration, examines a disk embedded in a homogeneous half-space, discusses the representation of the problem for analysis by a computer program, and describes an efficient recursive implementation of such a program, including MATLAB listings of the key functions.
Publisher Summary This chapter explains the model of initial cone with outward wave propagation i... more Publisher Summary This chapter explains the model of initial cone with outward wave propagation in vibration analysis. The chapter is limited to those relationships that are required to calculate the dynamic-stiffness coefficients and the effective foundation input motion. As the analysis is performed in the frequency domain, the derivation is also performed for harmonic excitation in the elastic medium. The first of the two building blocks used to calculate the vibrations of an embedded foundation consists of a disk embedded in a layered half-space, modeled as a double cone, with each cone exhibiting outward wave propagation. Such a model is shown in the chapter for the vertical degree of freedom. As a special case, the disk is placed on the surface of the half-space that leads to a one-sided cone model. The chapter discusses the translational one-sided cone. The hypotheses and construction of the one-dimensional strength-of-materials approach using a tapered bar with the cross-section increasing in the direction of wave propagation—as in a cone—is addressed. The chapter derives the analogous relationships for the rotational one-sided cone and addresses the modifications necessary for the vertical and rocking degrees of freedom when Poisson's ratio approaches 1/2 yielding an infinite dilatational-wave velocity. The chapter presents the dynamic-stiffness coefficients of a (circular) foundation on the surface of a homogeneous half space that are compared with the results of a rigorous analysis.
Computational Fluid and Solid Mechanics 2003, Vols 1 and 2, Proceedings, 2003
Publisher Summary In this chapter, a novel semianalytical approach to continuum mechanics, known ... more Publisher Summary In this chapter, a novel semianalytical approach to continuum mechanics, known as the “scaled-boundary finite-element” method, is introduced for elasto-static problems involving an unbounded axisymmetric domain subjected to general loading. The accuracy and efficiency of the scaled boundary finite-element solutions are examined in the chapter by comparison with analytical solutions for a rigid circular footing on the surface of a homogeneous half-space subjected to vertical, horizontal, moment, and torsion loading. It is shown that as the number of nodes used to discretize the boundary increases, the computed solutions converge to the analytical solutions rapidly. Using a boundary discretized with 61 nodes, the discrepancies between the scaled-boundary finite-element solutions and the analytical solutions are negligible for all load cases.
Many researchers have studied traffic-induced ground vibrations. It was found that traffic-induce... more Many researchers have studied traffic-induced ground vibrations. It was found that traffic-induced ground vibration might disturb occupants in nearby structures, often impede normal operation of sensitive equipment, and under extreme cases, might cause architectural damages in structures. Many codes and standard organizations specify allowable ground vibration levels in terms of peak ground acceleration (PGA) and/or peak particle velocity (PPV), or peak ground vibrations together with principal ground vibration frequency (PF) to limit vibration effects on structures, human and sensitive equipment. Many empirical ground motion attenuation relations were derived from field measurement. Since wave propagation is highly site dependent, these empirical relations obtained by different researchers on different sites could differ significantly. In this paper, dynamic responses of four structural models, namely a low-rise residential structure, an office building, a medium-rise building and a high-rise building to field measured traffic-induced ground vibrations are calculated. The largest dynamic structural response time history in each structural model is extracted. The floor level that the largest dynamic response occurs is identified. The peak acceleration and peak velocity response spectrum of each structural model are estimated and compared with the allowable vibration limits for structure damage, for human perception or disturbance and for sensitive equipment. It is found that traffic-induced ground vibration is not strong enough to cause damage to RC structures, but might disturb occupants in structures near a busy road, and is strong enough to cause malfunctioning of sensitive equipment. Therefore, proper isolation is needed for sensitive equipment housed in structures near roads.
The scaled boundary method is a semi-analytical method developed by Wolf and Song (1996) to deriv... more The scaled boundary method is a semi-analytical method developed by Wolf and Song (1996) to derive the dynamic stiffness matrices of unbounded domains. A virtual work derivation for elastostatics developed by Deeks and Wolf (2002) improved the accessibility of the method by reformulating the complicated mathematics of the original derivation.
The 70th anniversary of the International Association of Universities provides an opportunity to ... more The 70th anniversary of the International Association of Universities provides an opportunity to look back over the post-World War II era, and to reflect on the drivers that have led to the international higher education environment we experience today. The anniversary also provides an opportunity to look forward and to consider how such a globalised system of universities might contribute to future society.
Journal of Zhejiang University Science a Applied Physics Engineering, Mar 1, 2012
ABSTRACT Hollow core slabs are becoming of increasing interest as the construction industry attem... more ABSTRACT Hollow core slabs are becoming of increasing interest as the construction industry attempts to minimise the impact of its activities on the environment. By forming voids in the interior of a concrete slab, the amount of concrete used can be reduced without significantly altering the capacity of the structure. In this study, we examined the inner force transfer mechanism of a column-supported cast-in-situ hollow core slab using finite element analysis. Both a hollow core slab and the corresponding solid slab were analysed using ANSYS and the results were compared. The orientation of the tube fillers causes the stiffness of the hollow slab to be orthotropic, potentially changing the distribution of load carried in the two orthogonal directions. Both the cross-section’s moments in the column strip and near the columns in the hollow core slab become larger than that in the solid floor. As well, the cross-section’s stiffness along the tube arrangement direction is larger than that of the radial cross-section, which causes the direction along the hole of the hollow core slab to carry more moment than the radial direction. The conversion factors of the two directions are proposed from the comparison for four typical areas of the hollow core slab, as are the moment distribution coefficients.
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Papers by Andrew J Deeks