Mehdi Omidvar

Dynamic Response of Inextensible Beams by Improved Energy Balance Method

An improved Hes energy balance method (EBM) for solving non-linear oscillatory differential equation using a new trial function is presented. The problem considered represents the governing equations of the non-linear, large-amplitude free vibrations of a slender cantilever beam with a rotationally flexible root and carrying a lumped mass at an intermediate position along its span. Based on the simple EBM, the variational integral of the non-linear conservative system is established, and the Fourier series expansion is employed to address the governing algebraic equations. An alternate procedure for a particular value of the initial condition is then used to estimate the constants. This semi-analytical representation gives excellent approximations to the exact solutions for the whole range of the oscillation amplitude, reducing the respective error of angular frequency in comparison with the simple EBM. Two illustrative examples are considered in order to elucidate the methods described, and to reveal the improvements made by the modified method.

An Approximate Solution for Boundary Value Problems in Structural Engineering and Fluid Mechanics

Variational iteration method (VIM) is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics. These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory. Comparison is made between the exact solutions and the results of the variational iteration method (VIM). The results reveal that this method is very effective and simple, and that it yields the exact solutions. It was shown that this method can be used effectively for solving linear and nonlinear boundary value problems.

Past, Present, and Future of Transparent Soils

Transparent soils have evolved in the past two decades as a useful tool for the physical modeling of soil-structure interaction mechanisms, saturated-unsaturated hydraulic behavior, and thermal processes in soils. This paper traces the history of the development of transparent soil surrogates used in laboratory 1-g bench-scale and centrifuge tests to investigate a variety of geotechnical applications. Many notable papers that appear in this special issue of the journal on modeling with transparent soils are introduced throughout the review. The paper also looks into the future to anticipate where further advances and applications of these materials and complementary technologies may be expected.

Image-Based Lagrangian Analysis of Granular Kinematics

AbstractIn this paper, algorithms to describe mesoscale and microscale kinematics of granular flow using image analysis are described. At the mesoscale, digital image correlation (DIC) is employed to derive displacement fields, from which rigid body rotation and strains are calculated using continuum mechanics descriptions of kinematics. Moreover, Lagrangian and Eulerian trajectories are obtained from DIC analysis. At the microscale, individual particle kinematics is resolved using particle identification and tracking algorithms. Microscale analysis of kinematics is then performed using definitions of affine and nonaffine local motion. In order to demonstrate the application of the algorithms an experimental setup of pile penetration in a plane strain calibration chamber is presented. Mesoscale and microscale analysis is performed on high-resolution images acquired from incremental jacking of the pile. It is shown through analysis of captured images that the developed tools can be effectively employed in ...

Photonic doppler velocimetry for study of rapid penetration into sand

Quantitative description of the interaction of high-speed projectiles with soils is important for many engineering applications, and provides insights into high strain rate constitutive behavior. In this paper, a novel method known as photonic Doppler velocimetry (PDV), capable of producing time resolved velocity measurements, is adapted for the study of objects penetrating rapidly into sand. Fundamentals of PDV are described, and the applicability of the method is demonstrated by producing time-resolved velocity measurements of spherical projectiles penetrating Ottawa sand models at high velocities in the range of 300 m/s. Penetration tests demonstrate that PDV is capable of producing velocity measurements even after the penetrator has reached a depth well below the soil surface. Results of the tests confirmed that resistance to penetration increases as relative density of the sand deposit increases. Moreover, there appears to be a threshold penetration velocity in dense dry sand, below which resistance to penetration reduces considerably. A quantitative description of deceleration of penetrators in soils can be adequately provided for most of the penetration using a simple drag force model.

Visualizing Kinematics of Dynamic Penetration in Granular Media Using Transparent Soils

This paper describes a new method for quantitative analysis of dynamic penetration into granular media. The method is based on refractive index matching used to produce transparent synthetic soils. First, a procedure referred to as the embedded plane technique is introduced, to overcome limitations with laser illumination in high-speed photography. The technique consists of seeding an embedded plane with opaque particles sandwiched within the transparent soil to visualize in-plane granular kinematics. Details of sample preparation are presented, and other issues related to rapid penetration into index-matched media are discussed. High-speed image acquisition is introduced for transparent soils, and relevant target illumination techniques are described. Finally, improved digital image correlation methods are introduced and used to derive displacement fields. Shear and volumetric strains are then calculated. Analyses performed on acquired images are used to illustrate the applicability of these novel index-matching methods to the study of low-velocity penetration into granular media. The data illustrates that, for impact velocities considered in this study, the majority of lateral displacements during penetration are contained to approximately four projectile diameters from the penetration axis. Vertical displacements extend several penetrator diameters ahead of the penetrator. Moreover, penetration is accompanied by significant vertical afterflow. Finally, a region of dense sand forms ahead of the penetrator with a conical shape, which travels with the penetrator during penetration.

APPLICATION OF HOMOTOPY PERTURBATION AND VARIATIONAL ITERATION METHODS TO SIR EPIDEMIC MODEL

Children born are susceptible to various diseases such as mumps and chicken pox. These diseases are the most common form of infectious diseases. In recent years, scientists have been trying to devise strategies to fight against these diseases. Since vaccination is considered the most effective strategy against childhood diseases, the development of the framework that would predict the optimal vaccine coverage level needed to prevent the spread of diseases is crucial. The SIR model is a standard compartmental model that has been used to describe many epidemiological diseases. In this article, two methods namely homotopy perturbation method (HPM) and variational iteration method (VIM) are employed to compute an approximation to the solution of nonlinear system of differential equations governing the problem. The obtained results are compared with those obtained by Adomian decomposition method (ADM). This research reveals that although the obtained results are the same, HPM and VIM are much more robust, more convenient and efficient in comparison to ADM.

A Nonviscous Water-Based Pore Fluid for Modeling With Transparent Soils

A new low viscosity transparent soil recipe was introduced in this note for the physical modeling of geotechnical problems. Pore fluid is a water-based solution made of sodium-thiosulfate treated sodium-iodide. The soil surrogate is crushed fused quartz. Physical and mechanical properties of the proposed materials were summarized, including refractive index (RI) and viscosity of the pore fluid, as well as hydraulic conductivity and shear strength of the produced transparent soil. The main advantages of the proposed transparent soil over previous recipes include lower viscosity, lower sensitivity to temperature variations, and the ability to recycle the materials for use in multiple tests.

Conjugate stress approach for rankine seismic active earth pressure in cohesionless soils

AbstractThe Rankine classic earth pressure solution has been expanded for the calculation of seismic earth pressure on rigid retaining walls supporting cohesionless backfill. The expanded solution is based on the conjugate stress concept, without employing any additional assumptions. A single formulation is used for static and pseudostatic seismic analyses of active conditions. The equation accounts for sloping backfill, as well as wall inclination, and can readily accommodate layered soil profiles and the presence of groundwater, which require tedious analysis in commonly used methods. A closed-form expression, as opposed to the constant value commonly used in practice, has been derived for the soil-wall friction angle as a function of the inertial forces and problem geometry for a given pseudostatic acceleration. Seismic lateral pressure increases with depth, and the point of application of the resultant is calculated based on stratigraphy. Comparison of the formulation with the widely used Mononobe-Oka...

Review of high strain rate testing of granular soils

This review provides an overview of testing techniques related to high strain rate (HSR) loading of granular media, in support of the increasing interest in civilian and military applications related to transient loading on sand. The intrinsic properties of granular soils are shown to be rate dependent. The framework for assessing rate dependent behavior of granular soils is presented. Techniques for applying HSR loading including uniaxial and triaxial compression configurations are discussed. Critical issues related to inertial and wave propagation effects as well as boundary effects are highlighted. In addition, options for test setup and measuring response are described both with respect to capabilities and drawbacks. The most relevant studies are summarized, but gaps and inconsistencies remain in the available literature.