Applied Pressure Distribution Research Articles

Implicit differentiation-based reliability analysis for shallow shell structures with the Boundary Element Method

A novel methodology for evaluating the response sensitivities of shallow shell structures using the Boundary Element Method (BEM) is presented in this work. The implicit derivatives of the BEM formulations for shallow shell structures, with respect to the geometrical variables, such as curvature and thickness, have been derived for the first time and incorporated into an Implicit Differentiation Method (IDM). The IDM is employed in conjunction with the First Order Reliability Method (FORM) to evaluate the reliability of shallow shell structures. The accuracy of the IDM formulation is first validated against an analytical solution, with results showing a maximum difference of only 2.61%. The IDM was later validated against the Finite Difference Method (FDM), with results showing a maximum difference of only 0.11%. The IDM was also found to be significantly more efficient than the FDM, requiring 35% less CPU time when calculating sensitivities. This is further compounded by the fact that, unlike the FDM, the IDM does not require a step size. A numerical example featuring a circular shallow shell is used to demonstrate the application of the IDM-based FORM for assessing structural reliability. The uncertainty in curvature is set as a variable for the purpose of investigating its impact on reliability. The results of the reliability index obtained from the IDM-FORM are compared to the results obtained from FDM-FORM and were found to be very similar. An analysis of sensitivity is conducted to identify the most significant variables affecting reliability. It is found that uncertainties in curvature, thickness, and applied pressure distribution parameters have the largest impact on structural reliability. To demonstrate how the IDM could be used in practice, it was employed as gradient-based optimisation procedure featuring shallow-shell structures. The IDM was found to be a very efficient and accurate alternative to existing methods for calculating structural response sensitivities.

Multi-resolution wavelet basis for solving steady forced Korteweg\u2013de Vries model

A steady forced Korteweg–de Vries (fKdV) model which includes gravity, capillary, and pressure distributions is solved numerically using the wavelet Galerkin method. The anti-derivatives of Daubechies wavelets are developed as the basis of the solution subspaces for the mixed boundary condition type. Accuracy of numerical solutions can be improved by increasing the number of wavelet levels in the multi-resolution analysis. The theoretical result of convergence rate is also shown. The problem can be viewed as gravity-capillary wave flows over an applied pressure distribution. The flow regime can be characterized by subcritical, supercritical, and critical flows depending on the value of the Froude number. Trapped depression and elevation waves are found over the pressure distribution. For a near-critical flow regime, a generalized solitary wave with ripples is presented. This shows a capillary effect in balance to gravity and the pressure force on the free surface.

Multilayered Fabric Pressure Sensor for Real-Time Piezo-Impedance Imaging of Pressure Distribution

We developed a multilayer fabric pressure distribution sensor, sensor interface, and electrical impedance imaging system for real-time pressure distribution imaging. The new pressure distribution sensor consists of conductive elastic fabrics and layered polyurethane (PU) nanoweb containing air shells to increase its pressure sensitivity. The sensitivity and hysteresis of three fabric sensors with different layer structures were measured to compare their electromechanical properties as a pressure sensor. The sensor with one PU nanoweb layer sandwiched by two conductive elastic fabrics showed the best performance and was chosen for real-time pressure distribution imaging experiments. The imaging system acquired the electrical impedance data along the boundary of the sensor by injecting ac currents and measuring induced voltages on its boundary. This enabled the system to detect both piezo-resistance and piezo-capacitance changes in the sensing area of the sensor subject to a vertically applied pressure distribution on the top surface of the sensor. Applying an impedance image reconstruction algorithm to the collected boundary data, impedance images of the sensing area were reconstructed in real time, which corresponded to the applied pressure distribution. Quantitative analyses of reconstructed impedance images were performed to evaluate the overall performance of the developed multilayer fabric pressure distribution sensor. The fabric sensor and the imaging system provide a new way of quantitatively visualizing pressure distributions in real time.

Applied bearing pressure beneath a reinforced soil foundation used in a geosynthetic reinforced soil integrated bridge system

Geosynthetic reinforced soil integrated bridge system (GRS-IBS) design guidelines recommend the use of a reinforced soil foundation (RSF) to support the dead loads that are applied by the reinforced soil abutment and bridge superstructure, as well as any live loads that are applied by traffic on the bridge or abutment. The RSF is composed of high-quality granular fill material that is compacted and encapsulated within a geotextile fabric. Current GRS-IBS interim implementation design guidelines recommend the use of design methodologies for bearing capacity that are based around rigid foundation behavior, which yield a trapezoidal applied pressure distribution that is converted to a uniform applied pressure that acts over a reduced footing width for purposes of analysis. Recommended methods for determining the applied pressure distribution beneath the RSF for settlement analyses follow conventional methodologies for assessing the settlement of spread footings, which typically assume uniformly applied pressures beneath the base of the foundation that are distributed to the underlying soil layers in a fashion that can reasonably be modeled with an elastic-theory approach. Field data collected from an instrumented GRS-IBS that was constructed over a fine-grained soil foundation indicates that the RSF actually behaves in a fairly flexible way under load, yielding an applied pressure distribution that is not uniform or trapezoidal, and which is significantly different than what conventional GRS-IBS design methodologies assume. This paper consequently presents an empirical approach to determining the applied pressure distribution beneath the RSF in GRS-IBS construction. This empirical approach is a useful first step for researchers, as it draws important attention to this issue, and provides a framework for collecting meaningful field data on future projects which accurately capture real GRS-IBS foundation behavior.

Lubrication analysis and sub-surface stress field of an automotive differential hypoid gear pair under dynamic loading

Film thickness and sub-surface stress distribution in a highly loaded automotive differential hypoid gear pair are examined. A 4-Degree of Freedom torsional gear dynamics model, taking into account the torsional stiffness of the pinion and the gear shafts, is used in order to evaluate the contact load, the surface velocities and the contact radii of curvature of the mating teeth during a full meshing cycle. The torsional gear dynamics model takes into account both the geometric non-linearities of the system (backlash non-linearity) as well as the time varying properties (contact radii, meshing stiffness) and the internal excitations caused by geometrical imperfections of the teeth pair (static transmission error). The input torque used for the study of the film thickness and the sub-surface stress distribution corresponds to the region after the main resonance, where no teeth separation occurs. The contact conditions predicted by the gear dynamics are used as the input for the elastohydrodynamic elliptical point contact analysis. The lubricant film thickness, the corresponding pressure and surface traction distributions are obtained quasi-statically using the output load of the dynamic gear pair model. The variation of the induced sub-surface stress field is determined throughout a meshing cycle. Based on the sub-surface reversing orthogonal shear stresses, marginal differences occur when the viscous shear on the conjunctional surfaces are taken into account, which are mainly influenced by the applied pressure distribution. The numerical prediction of lubricant film thickness agrees reasonably well with that predicted using the well-established extrapolated oil film thickness formulae reported in the literature.

Real-time stability measurement system for postural control

A method for assessing balance, which was sensitive to changes in the postural control system is presented. This paper describes the implementation of a force-sensing platform, with force sensing resistors as the sensing element. The platform is capable of measuring destabilized postural perturbations in dynamic and static postural conditions. Besides providing real-time qualitative assessment, the platform quantifies the postural control of the subjects. This is done by evaluating the weighted center of applied pressure distribution over time. The objective of this research was to establish the feasibility of using the force-sensing platform to test and gauge the postural control of individuals. Tests were conducted in Eye Open and Eye Close states on Flat Ground (static condition) and the balance trainer (dynamic condition). It was observed that the designed platform was able to gauge the sway experienced by the body when subject's states and conditions changed.

Free surface flow under gravity and surface tension due to an applied pressure distribution: I Bond number greater than one-third

We consider steady free surface two-dimensional flow due to a localized applied pressure distribution under the effects of both gravity and surface tension in water of constant depth, and in the presence of a uniform stream. The fluid is assumed to be inviscid and incompressible, and the flow is irrotational. The behavior of the forced nonlinear waves is characterized by three parameters: the Froude number, F, the Bond number, τ > 1/3, and the magnitude and sign of the pressure forcing parameter ɛ. The fully nonlinear wave problem is solved numerically by using a boundary integral method. For small amplitude waves and F 1/3, there exists both elevation and depression waves. In some cases, a limiting configuration in the form of a trapped bubble occurs in the depression wave solutions.

Free surface flow under gravity and surface tension due to an applied pressure distribution II Bond number less than one-third

We consider the steady free surface two-dimensional flow due to a localized applied pressure distribution under the effects of both gravity and surface tension in water of a constant depth, and in the presence of a uniform stream. The fluid is assumed to be inviscid and incompressible, and the flow is irrotational. The behaviour of the forced nonlinear waves is characterized by three parameters: the Froude number, F, the Bond number, τ < 1 / 3 , and the magnitude and sign of the pressure forcing term ε. The fully nonlinear wave problem is solved numerically by using a boundary integral method. For small amplitude waves and F < F m < 1 where F m is a certain critical value where the phase and group velocities for linearized waves coincide, linear theory gives a good prediction for the numerical solution of the nonlinear problem in the case of a bifurcation from the uniform flow. As F approaches F m , nonlinearity needs to be included in the problem. In this case the forced nonlinear Schrödinger equation is found to be an appropriate model to describe bifurcations from an unforced envelope solitary wave. In general, it is found that for given values of F < F m and τ < 1 / 3 , there exist both elevation and depression waves.

A Useful Solution for Estimating Contact Pressure Between a Plate and Foundation

Many manufacturing situations involve a finite thickness plate or layer of material which is pressed against a much thicker foundation of the same or different material. One key example is a blank holder (plate) pressed against a die (foundation) in a sheet metal forming operation. In designing such a plate/foundation system the design objective often involves the contact stress distribution between the plate and foundation and the design variables are typically the thickness and modulus of the plate, the stiffness of the foundation and the applied pressure distribution on the noncontacting side of the plate. In general the problem relating the variables to the contact pressure distribution is three-dimensional and requires a complex finite element or boundary element solution. However, if the applied pressure distribution consists of sufficiently localized patches, which is often the case in applications, then an approximate 3D solution can be constructed by superposition. Specifically, the paper provides a convenient calculation procedure for the contact pressure due to a single circular patch of applied pressure on an infinite, isotropic, elastic layer which rests on a Winkler foundation. The procedure is validated by using known analytical solutions and the finite element method (FEM). Next a sensitivity study is presented for ascertaining the validity of the solution’s use in constructing solutions to practical problems involving multiple patches of loading. This is accomplished through a parametric study of the effects of loading radius, layer thickness, layer elastic properties, foundation stiffness and the form of the applied pressure distribution on the magnitude and extent of the contact pressure distribution. Finally, a procedure for determining an appropriate Winkler stiffness parameter for a foundation is presented. [S1087-1357(00)00603-1]

Dynamic Deformations of Circular Membranes

Equations of motion that govern the inelastic, large deformations of circular membranes subjected to blast loadings are derived and solved numerically. Good correlation with experimental results and with results of a related analytical study were obtained. Investigations were made into the effects of the applied pressure distribution and edge restraint on the final mechanical state of the deformed membrane.