Application of discontinuity layout optimization to plane plasticity problems

A new and potentially widely applicable numerical analysis procedure for continuum mechanics problems is described. The procedure is used here to determine the critical layout of discontinuities and associated upper-bound limit load for plane plasticity problems. Potential discontinuities, which interlink nodes laid out over the body under consideration, are permitted to crossover one another giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology. Highly efficient linear programming solvers can be employed when certain popular failure criteria are specified (e. g. Tresca or Mohr Coulomb in plane strain). Stress/velocity singularities are automatically identified and visual interpretation of the output is straightforward. The procedure, coined 'discontinuity layout optimization' (DLO), is related to that used to identify the optimum layout of bars in trusses, with discontinuities (e. g. slip-lines) in a translational failure mechanism corresponding to bars in an optimum truss. Hence, a recently developed adaptive nodal connection strategy developed for truss layout optimization problems can advantageously be applied here. The procedure is used to identify critical translational failure mechanisms for selected metal forming and soil mechanics problems. Close agreement with the exact analytical solutions is obtained

Rayleigh Wave Dispersion Curve Inversion: Occam Versus the L1-Norm

We compare inversions of Rayleigh wave dispersion curves for shear wave velocity depth profiles based on the L2-norm (Occam\u27s Inversion) and L1-norm (TV Regularization). We forward model Rayleigh waves using a finite-element method instead of the conventional technique based on a recursion formula and root-finding. The forward modeling naturally leads to an inverse problem that is overparameterized in depth. Solving the inverse problem with Occam\u27s Inversion gives the smoothest subsurface model that satisfies the data. However, the subsurface need not be smooth and we therefore also solve the inverse problem with TV Regularization, a procedure that does not penalize discontinuities. The use of such a regularization scheme for such an overparameterized inverse problem means blocky subsurface models can be obtained without fixing the layer boundaries in advance. This represents an entirely new philosophy for surface wave inversion

Effectiveness of PV Drains for Mitigating Earthquake-Induced Deformations in Sandy Slopes

This paper considers the effectiveness of a Pre-fabricated Vertical (PV) drain array for mitigating the earthquake-induced permanent ground deformations of a water-fronting loose sand fill based on results of numerical simulations. The numerical simulations are performed using the OpenSees finite element framework to represent the non-linear coupled ground deformation and transient pore pressures with customized 1-D finite elements to describe flow in the PV drains. Soil behavior is modeled using an advanced elasto-plastic effective stress soil model ("DM" for Dafalias & Manzari, 2004). The analyses focus on the performance of an 18.3m high sand fill, representative of many west-coast port facilities, and compare the response with and without the PV drain mitigation system for a suite of 58 reference seismic ground motions. The computed permanent slope deformations are well correlated with the peak ground accelerations (PGA) and especially the Arias intensity (I[subscript a]). The PV drain mitigation system is effective in reducing permanent lateral deformations at the crest of the slope by a factor of 1.2 - 3.5. The system effectiveness is largely independent of the characteristics of the ground motions. The damage results have been incorporated in slope fragility curves that can be used to quantify the expected costs from earthquake damage.National Science Foundation (U.S.) (Grant CMS-0530478)National Science Foundation (U.S.) (Network for Earthquake Engineering Simulation Research (NEESR) Challenge Project

Complex frequencies in elastodynamics, with application to the Damping-Solvent Extraction method

This paper addresses the use of complex frequencies in problems of wave propagation and structural vibrations. The most common form of application is as artificial damping that is extracted after the response in the time domain has been obtained. Then again a rather unorthodox application is in the simulation of systems of infinite spatial extent by means of finite systems modeled with discrete methods such as finite elements, a task that can be accomplished even when no transmitting or absorbing boundaries are used. This latter application of complex frequencies, which goes by the name damping-solvent extraction method or its acronym DSE, is assessed herein by means of exact solutions to canonical problems that are used to establish the conditions that must be met by the finite models to work as intended, especially the size of the models, the magnitude of the imaginary component of frequency, and the limitations of the method

Modelling rotational failure in confined geometries using DLO

Discontinuity layout optimisation (DLO) is a generally applicable numerical limit analysis procedure that can be used to identify critical plastic collapse mechanisms in engineering problems. Considering the modelling of in-plane failure, the authors have previously presented a formulation capable of identifying rotational failure mechanisms in non-dilating media. However, the formulation presented did not explicitly address cases involving confined geometries, where curved slip lines could potentially intersect boundaries. In this paper, methods are outlined which permit efficient modelling of such cases. Details of the kinematic and equilibrium formulations are provided, which are then verified through application to various geotechnical and structural mechanics problems. It is shown that results of high accuracy can be obtained, both in terms of the predicted collapse load and the corresponding failure mechanism

A higher order perfectly matched layer formulation for finite-difference time-domain seismic wave modeling

We have developed a higher order perfectly matched layer (PML) formulation to improve the absorption performance for finite-difference time-domain seismic modeling. First, we outlined a new unsplit “correction” approach, which allowed for traditional, first-order PMLs to be added directly to existing codes in a straightforward manner. Then, using this framework, we constructed a PML formulation that can be used to construct higher order PMLs of arbitrary order. The greater number of degrees of freedom associated with the higher order PML allow for enhanced flexibility of the PML stretching functions, thus potentially facilitating enhanced absorption performance. We found that the new approach can offer increased elastodynamic absorption, particularly for evanescent waves. We also discovered that the extra degrees of freedom associated with the higher order PML required careful optimization if enhanced absorption was to be achieved. Furthermore, these extra degrees of freedom increased the computational requirements in comparison with first-order schemes. We reached our formulations using one compact equation thus increasing the ease of implementation. Additionally, the formulations are based on a recursive integration approach that reduce PML memory requirements, and do not require special consideration for corner regions. We tested the new formulations to determine their ability to absorb body waves and surface waves. We also tested standard staggered grid stencils and rotated staggered grid stencils

Hybrid active focusing with adaptive dispersion for higher defect sensitivity in guided wave inspection of cylindrical structures

This is an Accepted Manuscript of an article published by Taylor & Francis in Nondestructive Testing and Evaluation on 23/11/2015, available online: https://www.tandfonline.com/doi/full/10.1080/10589759.2015.1093628.Ultrasonic guided wave inspection is widely used for scanning prismatic structures such as pipes for metal loss. Recent research has investigated focusing the sound energy into predetermined regions of a pipe in order to enhance the defect sensitivity. This paper presents an active focusing technique which is based on a combination of numerical simulation and time reversal concept. The proposed technique is empirically validated using a 3D laser vibrometry measurement of the focal spot. The defect sensitivity of the proposed technique is compared with conventional active focusing, time reversal focusing and synthetic focusing through an empirically validated finite element parametric study. Based on the results, the proposed technique achieves approximately 10 dB improvement of signal-to-coherent-noise ratio compared to the conventional active focusing and time reversal focusing. It is also demonstrated that the proposed technique to have an amplitude gain of around 5 dB over synthetic focusing for defects <0.5λs. The proposed technique is shown to have the potential to improve the reliably detectable flaw size in guided wave inspection from 9% to less than 1% cross-sectional area loss.TWI Ltd and the Center for Electronic System Research (CESR) of Brunel University

Hybrid active focusing with adaptive dispersion for higher defect sensitivity in guided wave inspection of cylindrical structures

This is an Accepted Manuscript of an article published by Taylor & Francis in Nondestructive Testing and Evaluation on 23/11/2015, available online: https://www.tandfonline.com/doi/full/10.1080/10589759.2015.1093628.Ultrasonic guided wave inspection is widely used for scanning prismatic structures such as pipes for metal loss. Recent research has investigated focusing the sound energy into predetermined regions of a pipe in order to enhance the defect sensitivity. This paper presents an active focusing technique which is based on a combination of numerical simulation and time reversal concept. The proposed technique is empirically validated using a 3D laser vibrometry measurement of the focal spot. The defect sensitivity of the proposed technique is compared with conventional active focusing, time reversal focusing and synthetic focusing through an empirically validated finite element parametric study. Based on the results, the proposed technique achieves approximately 10 dB improvement of signal-to-coherent-noise ratio compared to the conventional active focusing and time reversal focusing. It is also demonstrated that the proposed technique to have an amplitude gain of around 5 dB over synthetic focusing for defects <0.5λs. The proposed technique is shown to have the potential to improve the reliably detectable flaw size in guided wave inspection from 9% to less than 1% cross-sectional area loss.TWI Ltd and the Center for Electronic System Research (CESR) of Brunel University