Meshfree method analysis of Biot’s consolidation using the node-based smoothed point interpolation method (NS-PIM)

Purpose The purpose of the article is to extend the node-based smoothed point interpolation method (NS-PIM) for soil consolidation analysis based on the Biot’s theory. Design/methodology/approach The shape functions for displacements and pore pressures are constructed using the PIM separately, leading to the Kronecker delta property and easy implementation of essential boundary conditions. Then, a benchmark problem of 2D consolidation under ramp load is solved to investigate the validity of this application. Meanwhile, convergence features of different solutions are studied. Furthermore, the incompressible and impermeable condition under instant load is investigated. The results calculated by the NS-PIM solution with different orders of shape functions are compared. Finally a 2D consolidation problem in construction period is solved. An error estimation method is applied to check the mesh quality. Findings The results of the NS-PIM solution show good agreement with those certified results. Useful convergence features are found when comparing the results of the NS-PIM and the FEM solutions. A simple method is introduced to estimate the errors of the model with rough grids. The convergence features and error estimation method can be applied to check the mesh quality and get accurate results. More stable results can be obtained using the NS-PIM solution with lower order of pore pressure shape functions under the incompressible and impermeable condition. Research limitations/implications It cannot be denied that the calculation of NS-PIM solution takes more time than that of the FEM solution, and more work needs to be carried out to optimize the NS-PIM solution. Also, in further study, the feasibility of more complicated and practical engineering problems can still be probed in the NS-PIM solution. Practical implications This paper introduced a method for the consolidation analysis on the situation of construction loads (“ramp load”) using the NS-PIM which is quite indispensable in many foundation problems. Also, more stable results can be obtained using the NS-PIM solution with lower order of pore pressure shape functions than that with same order of shape functions. Originality/value This study first focuses on the situation of construction loads (“ramp load”) in the NS-PIM consolidation analysis which is quite indispensable in many foundation problems. An error estimation method is introduced to evaluate the mesh quality and get accurate values based on the convergence features of the FEM and NS-PIM solutions. Then, the incompressible and impermeable condition under instant load is investigated, and the analysis show that the NS-PIM with lower order of pore pressure shape functions can get stable results in such conditions.

Analytical Solution for One-Dimensional Consolidation of Soil with Exponentially Time-Growing Drainage Boundary under a Ramp Load

By introducing the exponentially time-growing drainage boundary, this paper investigated the one-dimensional consolidation problem of soil under a ramp load. Firstly, the one-dimensional consolidation equations of soil are established when there is a ramp load acting on the soil surface. Then, the analytical solution of excess pore water pressure and consolidation degree is derived by means of the method of separation of variables and the integral transform technique. The rationality of this solution is also verified by comparing it with other existing analytical solutions. Finally, the consolidation behavior of soil is studied in detail for different interface parameters or loading scheme. The results show that the exponentially time-growing drainage boundary can reflect the phenomenon that the excess pore water pressure at the drainage boundaries dissipates smoothly rather than abruptly from its initial value to the value of zero. By adjusting the values of interface parameters b and c, the presented solution can be degraded to Schiffman’s solution, which can compensate for the shortcoming that Terzaghi’s drainage boundary can only consider the two extreme cases of fully pervious and impervious boundaries. The significant advantage of the exponentially time-growing drainage boundary is that it can be applied to describe the asymmetric drainage characteristics of the top and bottom drainage surfaces of the actual soil layer by choosing the appropriate interface parameters b and c.

Influence of the Wave Form on the Material Response Delay

To model damping effects in structural dynamics, the literature provides a wide range of alternatives. The different models claim different advantages and fields of use where they are useful but, in the end, the compliance of the model with the experimental results, within a given tolerance, is the ultimate criterion for assessing its quality. In the present paper, the behaviour of a simple steel specimen is studied, taking as a focus the time response of the material. Since the harmonic response is well established, the authors propose to submit the specimen to a trapezoidal periodic load and study the behaviour of the response to the load changes. A simple setup was used, using a steel specimen loaded in the linear regime. A carefull test procedure was carried out in order to characterize the dissipation in a quasi-static periodic load. The experimental results show that the response delay to a ramp load depends on the durations of both the previous flat and the ramp itself.

Illusion caused by vibration of muscle spindles reveals an involvement of muscle spindle inputs in regulating isometric contraction of masseter muscles

Spindle Ia afferents may be differentially involved in voluntary isometric contraction, depending on the pattern of synaptic connections in spindle reflex pathways. We investigated how isometric contraction of masseter muscles is regulated through the activity of their muscle spindles that contain the largest number of intrafusal fibers among skeletal muscle spindles by examining the effects of vibration of muscle spindles on the voluntary isometric contraction. Subjects were instructed to hold the jaw at resting position by counteracting ramp loads applied on lower molar teeth. In response to the increasing-ramp load, the root mean square (RMS) of masseter EMG activity almost linearly increased under no vibration, while displaying a steep linear increase followed by a slower increase under vibration. The regression line of the relationship between the load and RMS was significantly steeper under vibration than under no vibration, suggesting that the subjects overestimated the ramp load and excessively counteracted it as reflected in the emergence of bite pressure. In response to the decreasing-ramp load applied following the increasing one, the RMS hardly decreased under vibration unlike under no vibration, leading to a generation of bite pressure even after the offset of the negative-ramp load until the vibration was ceased. Thus the subjects overestimated the increasing rate of the load while underestimating the decreasing rate of the load, due to the vibration-induced illusion of jaw opening. These observations suggest that spindle Ia/II inputs play crucial roles both in estimating the load and in controlling the isometric contraction of masseter muscles in the jaw-closed position.

Commutational Output Feedback Control for Disk Drive Ramp Loading

The feasibility of a ramp load controller using a conventional disk drive actuator is investigated. The controller eliminates the necessity of increased material requirements common in ramp load disk drives. Therefore, disk drives with lower cost, higher performance actuators can realize the linear shock protection benefits of ramp loading. A disk drive designed with a conventional actuator is outfitted with a ramp and optimized for ramp load operation. While on the ramp, there exists a set in the state space where the actuator dynamics are uncontrollable. An input commutation is required within the uncontrollable region to sustain the direction of actuator motion. Additionally, the motor torque factor, magnetic restoration bias, and friction torque are nonlinear and can be represented by functions that are Lipschitz within the actuator ramp angle. A state trajectory is generated that, when tracked, moves the actuator through the uncontrollable set for a successful load onto the disk at the desired load velocity. Because position and velocity information are not available during a load maneuver, an output feedback controller is necessary. A stable, output feedback tracking controller is designed to track the trajectory and handle the nonlinear effects. A unique disk drive is manufactured and experiments are performed to verify the complete ramp loading design strategy.