Complex Variable Solution for Stress and Displacement of Layered Soil with Finite Thickness

The static problem of a layered isotropic elastic body is a very useful research subject in relation to the analysis and design of foundation works. Due to the complexity of the problem, there is no analytical solution to the problem so far. This study provides an efficient analytical approach to accurately calculate the displacement and stress fields of the soil. The constraints of bedrock on soil, different soil layer thickness and the shear stress of the foundation on soil were all taken into account in the analysis. In this study, each layer is regarded as an isotropic elastomer with infinite width, and the layers are in complete contact. By using conformal mapping, each layer is mapped to a unit circle, and the two complex potential functions are expanded into Taylor series with unknown coefficients. These unknown coefficients are obtained by satisfying boundary conditions and continuity conditions. The boundary and continuity conditions were verified in this paper. As a validation step, we compared the analytical results for the settlement with the results of the ANSYS numerical simulations and found good agreement. Parametric analyses were also carried out to investigate the influence of different distribution forms of base pressure on surface settlement, and the effects of layered properties on the surface settlement and stress field.

A Quasi-Brittle damage model in the framework of Bond-based Peridynamics with Adaptive Dynamic Relaxation method

Peridynamics (PD) is a new tool, based on the non-local theory for modelling fracture mechanics, where particles connected through physical interaction used to represent a domain. By using the PD theory, damage or crack in a material domain can be shown in much practical representation. This study compares between Prototype Microelastic Brittle (PMB) damage model and a new Quasi-Brittle (QBR) damage model in the framework of the Bond-based Peridynamics (BBPD) in terms of the damage plot. An in-house code using Matlab was developed for BBPD with inclusion of both damage models, and tested for a quasi-static problem with the implementation of Adaptive Dynamic Relaxation (ADR) method in the theory in order to get a faster steady state solutions. This paper is the first attempt to include ADR method in the framework of BBPD for QBR damage model. This paper analysed a numerical problem with the absence of failure and compared the displacement with literature result that used Finite Element Method (FEM). The obtained numerical results are in good agreement with the result from FEM. The same problem was used with the allowance of the failure to happen for both of the damage models; PMB and QBR, to observe the damage pattern between these two damage models. PMB damage model produced damage value of roughly twice compared to the damage value from QBR damage model. It is found that the QBR damage model with ADR under quasi-static loading significantly improves the prediction of the progressive failure process, and managed to model a more realistic damage model with respect to the PMB damage model.

An Elastic Half Space with a Moving Punch

The dynamic problem of a punch with rounded tips moving in an elastic half-space in a fixed direction has been considered. The static problem of determining stress component under the contact region of a punch has also been solved. Fourier integral transform has been employed to reduce the problems in solving dual integral equations. These integral equations have been solved using Cooke’s [1] result (1970) to obtain the stress component. Finally, exact expressions for stress components under the punch and the normal displacement component in the region outside the punch have been derived. Numerical results for stress intensity factor at the punch end and torque applied over the contact region have been presented in the form of graph.

Iterative technique for a beam lying on a transversely isotropic foundation

The effect of the foundation heterogeneity on the mechanical behaviour of a beam on Vlasov soils is discussed. According to a refined Vlasov soil model, the static problem of beams lying on transversely isotropic soils can be solved by an iterative method. In this paper, based on the energy variational principle, the differential equations for beams under an axial force on refined Vlasov foundations are derived. The methods for solving the internal forces and deformations of beams lying on refined elastic foundations are given. Additionally, an equation for the attenuation parameters is also established, and the characteristic parameters of the refined model are solved by iterative technique. Numerical results show that the foundation heterogeneity have a influence on the deformations and internal forces of the beam-soil system. Moreover, relatively accurate characteristic parameters can be obtained through the iterative process. The refined Vlasov model has broad application prospects.

On the Development of a Multi-Layered Agent-Based Heurisitc System for Vehicle Routing Problem under Random Vehicle Breakdown

With the recent technological advancement, the Dynamic Vehicle Routing Problem (DVRP) is becoming more applicable but almost all of the research in this field limited the source of dynamism from the order side rather from the vehicle, in addition to the adoption of inflexible tools that are mainly designed for the static problem. Considering multiple random vehicle breakdowns complicates the problem of how to adapt and distribute the workload to other functioning vehicles. In this ongoing PhD research, a proposed multi-layered Agent-Based Model (ABM) along with a modelling framework on how to deal with such disruptive events in a reactive continuous manner. The model is partially constructed and experimented, with a developed clustering rule, on two randomly generated scenario for the purpose of validation. The rule achieved good order allocation to vehicles and reacted to different problem sizes by rejecting orders that are over the model capacity. This shows a promising path in fully adopting the ABM model in this dynamic problem.

Steady Fluid–Structure Coupling Interface of Circular Membrane under Liquid Weight Loading: Closed-Form Solution for Differential-Integral Equations

In this paper, the problem of fluid–structure interaction of a circular membrane under liquid weight loading is formulated and is solved analytically. The circular membrane is initially flat and works as the bottom of a cylindrical cup or bucket. The initially flat circular membrane will undergo axisymmetric deformation and deflection after a certain amount of liquid is poured into the cylindrical cup. The amount of the liquid poured determines the deformation and deflection of the circular membrane, while in turn, the deformation and deflection of the circular membrane changes the shape and distribution of the liquid poured on the deformed and deflected circular membrane, resulting in the so-called fluid-structure interaction between liquid and membrane. For a given amount of liquid, the fluid-structure interaction will eventually reach a static equilibrium and the fluid-structure coupling interface is steady, resulting in a static problem of axisymmetric deformation and deflection of the circular membrane under the weight of given liquid. The established governing equations for the static problem contain both differential operation and integral operation and the power series method plays an irreplaceable role in solving the differential-integral equations. Finally, the closed-form solutions for stress and deflection are presented and are confirmed to be convergent by the numerical examples conducted.

On the statics and dynamics of granular-microstructured rods with higher order effects

Granular-microstructured rods show strong dependence of grain-scale interactions in their mechanical behavior, and therefore, their proper description requires theories beyond the classical theory of continuum mechanics. Recently, the authors have derived a micromorphic continuum theory of degree n based upon the granular micromechanics approach (GMA). Here, the GMA is further specialized for a one-dimensional material with granular microstructure that can be described as a micromorphic medium of degree 1. To this end, the constitutive relationships, governing equations of motion and variationally consistent boundary conditions are derived. Furthermore, the static and dynamic length scales are linked to the second-gradient stiffness and micro-scale mass density distribution, respectively. The behavior of a one-dimensional granular structure for different boundary conditions is studied in both static and dynamic problems. The effects of material constants and the size effects on the response of the material are also investigated through parametric studies. In the static problem, the size-dependency of the system is observed in the width of the emergent boundary layers for certain imposed boundary conditions. In the dynamic problem, microstructural effects are always present and are manifested as deviations in the natural frequencies of the system from their classical counterparts.

Density–orientation coupling for a microcontinuum approach to nematic liquid crystals subject to electric field

A microcontinuum description of compressible liquid crystals is examined accounting for a constitutive model based on mass microdensity. As a first point, we discuss the effectiveness of the micropolar theory on compressible continua, which is limited to static problems. Then, by a micromorphic representation of mass density, we show the consistence of some classical constitutive models for compressible nematic liquid crystals and remark their connection with the microinertia tensor. After the analysis of a constitutive micropolar model, we discuss a static problem for a layer of compressible nematic liquid crystal in a planar configuration. The effects of an applied electric potential are considered remarking the coupling of density distribution with the molecular orientation.

Dynamic model of the software development market based on the assignment problem on pain points

The authors propose the formulation of a discrete dynamic model of the software developmentmarket (SM) based on the assignment problem (AP) on pain points (PP), which can also be obtained according to the scheme used in (Vasin, Grigorieva, Lesik, 2018), if we abandon the integer number of elements of the assignment matrix. However, there are also features: equilibrium prices can be calculated directly, and therefore a variational formulation of the internal problem of determining equilibrium prices based on Debreu's theorem (Debreu, 1954) is not required. The functions of changing the phase coordinates can be taken convex, for example, the norm of the difference in the square, and do not take into account the constant costs for each control switching. Such a statement is also given in this paper. If we have a dynamic expansion of the AP on PP, it is possible to determine the additional profit of the transport system through the use of futures. Formulas for the components of the gradient of the indicator are obtained. This allows us to organize a gradient method for solving a dynamic AP on PP. The authors also demonstrate an approximate algorithm and a model example of its use for solving the dynamic expansion of the AP on PP, based on solving the current static problem with an increment of those elements of the efficiency matrix that coincide with the corresponding elements of the optimal assignment matrix, if we abandon the integer nature of the assignment matrix. This is equivalent to randomization of the assignment problem, when the corresponding assignments are implemented with certain probabilities, which are used to determine the error of the approximate algorithm by comparing it with the exact solution obtained with the gradient method for sufficiently large values of penalty constants.