Efficient solution of multiple cracks in great number using eigen COD boundary integral equations with iteration procedure

A newly developed computational approach is proposed in the paper for the analysis of multiple crack problems based on the eigen crack opening displacement (COD) boundary integral equations. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix to determine all the unknown CODs step by step. To deal with the interactions among cracks for multiple crack problems, all cracks in the problem are divided into two groups, namely the adjacent group and the far-field group, according to the distance to the current crack in consideration. The adjacent group contains cracks with relatively small distances but strong effects to the current crack, while the others, the cracks of far-field group are composed of those with relatively large distances. Correspondingly, the eigen COD of the current crack is computed in two parts. The first part is computed by using the fictitious tractions of adjacent cracks via the local Eshelby matrix derived from the traction boundary integral equations in discretized form, while the second part is computed by using those of far-field cracks so that the high computational efficiency can be achieved in the proposed approach. The numerical results of the proposed approach are compared not only with those using the dual boundary integral equations (D-BIE) and the BIE with numerical Green's functions (NGF) but also with those of the analytical solutions in literature. The effectiveness and the efficiency of the proposed approach is verified. Numerical examples are provided for the stress intensity factors of cracks, up to several thousands in number, in both the finite and infinite plates.

A new type of high-order elements based on the mesh-free interpolations

We propose a new type of high-order elements that incorporates the mesh-free Galerkin formulations into the framework of finite element method. Traditional polynomial interpolation is replaced by mesh-free interpolations in the present high-order elements, and the strain smoothing technique is used for integration of the governing equations based on smoothing cells. The properties of high-order elements, which are influenced by the basis function of mesh-free interpolations and boundary nodes, are discussed through numerical examples. It can be found that the basis function has significant influence on the computational accuracy and upper-lower bounds of energy norm, when the strain smoothing technique retains the softening phenomenon. This new type of high-order elements shows good performance when quadratic basis functions are used in the mesh-free interpolations and present elements prove advantageous in adaptive mesh and nodes refinement schemes. Furthermore, it shows less sensitive to the quality of element because it uses the mesh-free interpolations and obeys the Weakened Weak (W2) formulation as introduced in [3, 5].

Effective shear modulus approach for two dimensional solids and plate bending problems by meshless point collocation method

For the analysis of material nonlinearity, an effective shear modulus approach based on the strain control method is proposed in this paper by using point collocation method. Hencky’s total deformation theory is used to evaluate the effective shear modulus, Young’s modulus and Poisson’s ratio, which are treated as spatial field variables. These effective properties are obtained by the strain controlled projection method in an iterative manner. To evaluate the second order derivatives of shape function at the field point, the radial basis function (RBF) in the local support domain is used. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method and comparisons have been made with analytical solutions and the finite element method (ABAQUS).

Fluid-structure interaction analysis of full scale vehicle-barrier impact using coupled SPH-FEA

Portable water-filled barriers (PWFB) are roadside structures used to separate moving traffic from work-zones. Numerical PWFB modelling is preferred in the design stages prior to actual testing. This paper aims to study the fluid-structure interaction of PWFB under vehicular impact using several methods. The strategy to treat water as non-structural mass was proposed and the errors were investigated. It was found that water can be treated with the FEA-NSM model for velocities higher than 80kmh-1. However, full SPH/FEA model is still the best treatment for water and necessary for lower impact velocities. The findings in this paper can be used as guidelines for modelling and designing PWFB.

Simulation of plant cell shrinkage during drying : A SPH–DEM approach

Plant based dried food products are popular commodities in global market where much research is focused to improve the products and processing techniques. In this regard, numerical modelling is highly applicable and in this work, a coupled meshfree particle-based two-dimensional (2-D) model was developed to simulate micro-scale deformations of plant cells during drying. Smoothed Particle Hydrodynamics (SPH) was used to model the viscous cell protoplasm (cell fluid) by approximating it to an incompressible Newtonian fluid. The visco-elastic characteristic of the cell wall was approximated to a Neo-Hookean solid material augmented with a viscous term and modelled with a Discrete Element Method (DEM). Compared to a previous work [H. C. P. Karunasena, W. Senadeera, Y. T. Gu and R. J. Brown, Appl. Math. Model., 2014], this study proposes three model improvements: linearly decreasing positive cell turgor pressure during drying, cell wall contraction forces and cell wall drying. The improvements made the model more comparable with experimental findings on dried cell morphology and geometric properties such as cell area, diameter, perimeter, roundness, elongation and compactness. This single cell model could be used as a building block for advanced tissue models which are highly applicable for product and process optimizations in Food Engineering.

Vibration characteristics of plate elements subjected in-plane loads (axial loads)

Axial deformations resulting from in-plane loads (axial forces) of plate elements impact significantly on their vibration characteristics. Although, numerous methods have been developed to quantify axial forces and hence deformations of individual plate elements with different boundary conditions based on their natural frequencies, these methods are unable to apply to the plate elements in a structural system. This is because the natural frequency is a global parameter for the entire structure. Thus, this paper proposes a comprehensive vibration based procedure to quantify axial deformations of plate elements in a structural framing system. Unique capabilities of the proposed method present through illustrative examples. Keywords- Plate Elements, Dynamic Stiffness Matrix, Finite Element Method, Vibration Characteristics, Axial Deformation

Quantifying in-plane deformation of plate elements using vibration characteristics

Plate elements are used in many engineering applications. In-plane loads and deformations have significant influence on the vibration characteristics of plate elements. Numerous methods have been developed to quantify the effects of in-plane loads and deformations of individual plate elements with different boundary conditions based on their natural frequencies. However, these developments cannot be applied to the plate elements in a structural system as the natural frequency is a global parameter for the entire structure. This highlights the need for a method to quantify in-plane deformations of plate elements in structural framing systems. Motivated by this gap in knowledge, this research has developed a comprehensive vibration based procedure to quantify in-plane deformation of plate elements in a structural framing system. This procedure with its unique capabilities to capture the influence of load migration, boundary conditions and different tributary areas is presented herein and illustrated through examples.

Boundary weaving : the social structure and processes of organizational boundaries

Boundaries are an important field of study because they mediate almost every aspect of organizational life. They are becoming increasingly more important as organizations change more frequently and yet, despite the endemic use of the boundary metaphor in common organizational parlance, they are poorly understood. Organizational boundaries are under-theorized and researchers in related fields often simply assume their existence, without defining them. The literature on organizational boundaries is fragmented with no unifying theoretical basis. As a result, when it is recognized that an organizational boundary is "dysfunctional". there is little recourse to models on which to base remediating action. This research sets out to develop just such a theoretical model and is guided by the general question: "What is the nature of organizational boundaries?" It is argued that organizational boundaries can be conceptualised through elements of both social structure and of social process. Elements of structure include objects, coupling, properties and identity. Social processes include objectification, identification, interaction and emergence. All of these elements are integrated by a core category, or basic social process, called boundary weaving. An organizational boundary is a complex system of objects and emergent properties that are woven together by people as they interact together, objectifying the world around them, identifying with these objects and creating couplings of varying strength and polarity as well as their own fragmented identity. Organizational boundaries are characterised by the multiplicity of interconnections, a particular domain of objects, varying levels of embodiment and patterns of interaction. The theory developed in this research emerged from an exploratory, qualitative research design employing grounded theory methodology. The field data was collected from the training headquarters of the New Zealand Army using semi-structured interviews and follow up observations. The unit of analysis is an organizational boundary. Only one research context was used because of the richness and multiplicity of organizational boundaries that were present. The model arose, grounded in the data collected, through a process of theoretical memoing and constant comparative analysis. Academic literature was used as a source of data to aid theory development and the saturation of some central categories. The final theory is classified as middle range, being substantive rather than formal, and is generalizable across medium to large organizations in low-context societies. The main limitation of the research arose from the breadth of the research with multiple lines of inquiry spanning several academic disciplines, with some relevant areas such as the role of identity and complexity being addressed at a necessarily high level. The organizational boundary theory developed by this research replaces the typology approaches, typical of previous theory on organizational boundaries and reconceptualises the nature of groups in organizations as well as the role of "boundary spanners". It also has implications for any theory that relies on the concept of boundaries, such as general systems theory. The main contribution of this research is the development of a holistic model of organizational boundaries including an explanation of the multiplicity of boundaries . no organization has a single definable boundary. A significant aspect of this contribution is the integration of aspects of complexity theory and identity theory to explain the emergence of higher-order properties of organizational boundaries and of organizational identity. The core category of "boundary weaving". is a powerful new metaphor that significantly reconceptualises the way organizational boundaries may be understood in organizations. It invokes secondary metaphors such as the weaving of an organization's "boundary fabric". and provides managers with other metaphorical perspectives, such as the management of boundary friction, boundary tension, boundary permeability and boundary stability. Opportunities for future research reside in formalising and testing the theory as well as developing analytical tools that would enable managers in organizations to apply the theory in practice.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.