Journal of Engineering Mechanics

Peridynamic (PD) theory is an integral-type nonlocal continuum mechanics theory that reformulates the equation of motion in local continuum mechanics as an integrodifferential equation. PD theory has been used to simulate mechanical responses of various materials with discontinuous structures. During the past two decades, PD theory has been developed to simulate different discontinuous problems and to illustrate various discontinuous phenomena in the diverse fields of engineering and sciences. In this paper, a state-of-the-art review on the investigation of failure processes of geomaterials in a PD framework is performed to illustrate the successful results and potential capability of PD theory in future geotechnical engineering. This review starts with a brief theoretical description of a bond-based peridynamic (BB-PD) model, a state-based peridynamic (SB-PD) model, a hybrid PD–classical continuum mechanics model, and an analytical PD model. Then surveys of PD applications to coupled multiphysical failure problems of geomaterials are conducted, which aim at revealing the associated failure mechanism. The applications of PD theory to simulate real geotechnical engineering are subsequently reported. Finally, some future-oriented research perspectives of PD applications in geotechnical engineering and a brief summary are presented.

The authors propose a seismic monitoring framework for instrumented buildings that employs dissipated energy as a feature for damage detection and localization. The proposed framework employs a nonlinear model-based state observer that combines a nonlinear finite element model of a building and global acceleration measurements to estimate the time history of the seismic response at all of the model’s degrees of freedom. This includes displacements, element forces, and plastic deformations in all structural members. The estimated seismic response is then used to (1) estimate interstory drifts and determine the postearthquake reoccupancy classification of the building based on performance-based criteria, (2) compare the estimated demands with code-based capacity and reconstruct element-by-element demand-to-capacity ratios, and (3) reconstruct element-level normalized energy dissipation and ductility. The outcome of this process is employed for performance-based monitoring, damage detection, and localization in instrumented buildings. The proposed framework is validated using data from the Van Nuys hotel testbed, a seven-story reinforced concrete building instrumented by the California Strong Motion Instrumentation Program (Station 24386). The nonlinear state observer of the building was implemented using a distributed plasticity finite element model and seismic response measurements during the 1992 Big Bear and 1994 Northridge earthquakes. The performance and damage assessment results are compared with the postearthquake damage inspection reports and photographic records. The results demonstrate the accuracy and capability of the proposed framework in the context of a real-world instrumented building that experienced significant localized structural damage.

The loading and response of structures due to gust buffeting is a dominant topic of wind engineering. One of its crucial aspects is the shape of vibration modes. Although numeric solutions are available for any mode, conceptual interpretations and closed-form solutions mainly are limited to the case in which the sign of the mode does not change along the structural axis. For modes that change sign, it is difficult, if not impossible, to recognize the physical role of the parameters that govern the problem and judge analysis results in qualitative form. This paper addressed this issue in the framework of quasi-steady theory by clarifying the relationship linking aerodynamic admittance with mode shape, showed that any mode may be brought back to a piecewise ensemble of regular modes with constant sign, and used this concept to obtain a closed-form expression for any aerodynamic admittance. This solution is simple for modes with few changes of sign, but becomes laborious as mode complexity increases. In addition, it provides a partial conceptual interpretation. Both of these limits were overcome in the companion paper, in which the use of proper orthogonal decomposition led to a full conceptual interpretation of aerodynamic admittance and a simple and general closed-form solution.

Studies carried out on gust buffeting and aerodynamic admittance show that mode shape represents a sort of watershed. If the mode does not change sign along the structure axis, the problem admits a robust conceptual interpretation based on energy cascade and a simple closed-form solution. If, instead, the mode changes sign, the solution calls for numerical tools, and its physical interpretation definitely is unclear. The companion paper investigated this issue within the novel framework of the enhanced equivalent spectrum technique and derived a closed-form solution of the aerodynamic admittance that can be applied to any mode using quasi-steady theory. This solution is precise and simple for modes with a few changes of sign, but it becomes laborious with increasing mode shape complexity; in addition, it provides a partial conceptual interpretation. Both these limitations were overcome in this paper, in which the application of proper orthogonal decomposition led to a full conceptual interpretation of aerodynamic admittance and to a simple and general closed-form solution. Analyses were limited here to single modes; multiple arbitrary modes are left for future research, as is the generalization of these concepts to arbitrary influence functions.

This technical note presents a pair of formulas to rotate a unit vector to another unit vector and compute the corresponding angular velocity. These formulas arose independently in two of our recent applications: (1) modeling actuator kinematics in a two-degree-of freedom (2-DOF) shaker, and (2) implementation of Kirchhoff rod theory in three-dimensional (3D) for modeling intracranial aneurysm coiling and analysis of electrical conductor nonlinear dynamics. The first formula (for rotation) can be found in the literature. The second formula (for angular velocity), while simple and straightforward, is not found in the literature and is the contribution in this note. This latter formula, due to its simplicity, is likely useful in a number of other applications in computational mechanics and mechanism/robot kinematics.

A simple formula for the resistance experienced by an arbitrary cylinder in Darcy flow is presented. This formula is then applied to elliptic cylinders in uniform flow as well as flow due to a source outside a circular cylinder. These applications are important for estimating the resistance of piles and drill strings due to groundwater movement.