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A meshless approach, collocation discrete least square (CDLS) method, is extended in this paper, for solving

elasticity problems. In the present CDLS method, the problem domain is discretized by distributed field nodes. The field

nodes are used to construct the trial functions. The moving least-squares interpolant is employed to construct the trial

functions. Some collocation points that are independent of the field nodes are used to form the total residuals of the

problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of the

residuals for the collocation points. The final stiffness matrix is symmetric and therefore can be solved via efficient

solvers. The boundary conditions are easily enforced by the penalty method. The present method does not require any

mesh so it is a truly meshless method. Numerical examples are studied in detail, which show that the present method

is stable and possesses good accuracy, high convergence rate and high efficiency.

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An important concern in rock mechanics is non-homogeneity as joints or fault. This noticeable feature of failures in rock is

appearance of slip surfaces or shear bands, the characteristics of that are associated with deformation being concentrated in a

narrow zones and the surrounding material remaining intact. Adopting the joints as fractures, fractures are well known for their

effects on the mechanical and transport properties of rock. A damaged pro-elasticity multi-plane based model has been developed

and presented to predict rock behavior. In this multi-plane model, the stress–strain behavior of a material is obtained by

integrating the mechanical response of an infinite number of predefined oriented planes passing through a material point.

Essential features such as the pro-elasticity hypothesis and multi-plane model are discussed. The methodology to be discussed

here is modeling of slip on the local and global levels due to the deformation procedure of the existing/probable joints of rock and

this method has a potential of using different parameters on different sampling planes to predict inherent anisotropy of rocks.

Upon the presented methodology, more attention has been given to slip initiation and propagation through these joints. In

particular, softening in non-linear behavior of joints in going from the peak to residual strengths imparts a behavior often

associated with progressive failure. The predictions of the derived stress–strain model are compared to experimental results for

marble, sandstone, Quartz mica schist and anisotropic schist. The comparisons demonstrate the capability of this model to

reproduce accurately the mechanical behavior of rocks.

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This paper aims to characterize the elastic modulus of structural modified normal density (MND) and lightweight aggregate concrete (LWAC) produced with different types of expanded clay lightweight aggregates (LWA). A comprehensive experimental study was carried out involving different concrete strengths ranging from 30 to 70 MPa and density classes D1.6 to D2.0. The influence of several factors on the LWAC elastic modulus, such as the cement content, initial wetting conditions, type and volume of coarse LWA and the partial replacement of normal weight coarse and fine aggregates by LWA are analyzed. The strength and deformability of LWAC seems to be little affected by the addition of high reactive nanosilica. Reasonable correlations are found between the elastic modulus and the compressive strength or concrete density. The obtained LWAC elastic moduli are compared with those reported in the literature and those estimated from the main normative documents. In general, codes underestimate the LWAC modulus of elasticity by less than 20%. However, the MND modulus of elasticity can be greatly underestimated. In addition, the prediction of LWAC elastic modulus by means of non-destructive ultrasonic tests is studied. Dynamic elasticity modulus and ultrasonic pulse velocity results are reported and high correlated relationships, over 0.95, with the static modulus are established.

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The determination of the parameters of concrete (i.e., elasticity modulus, tensile strength) is very crucial task in material engineering. For this purpose, in general, structural codes propose some empirical formulas to estimate the parameters of materials and is useful for designers rather than the experimental process. However, the estimated results usually vary for different standards. Hence, this research paper aims to compare the elasticity modulus formulas considering six standards (TS 500, ACI 318M-05, CSA A23.3-04, SP 52-101-2003, EN 1992-1-1 and AS-3600-2001) with experimental elasticity modulus test results. In the evaluation of the results, the TS 500 and EN-1992-1-1 overestimate the elasticity modulus and the SP-52-101-2003 estimates the values more close to experimental results. In addition, a new equation for modulus of elasticity including the compressive strength and the density is derived for RAC. Also, in this paper energy capacities of concretes (elastic energy capacity, plastic energy capacity and toughness) are evaluated considering compressive strength test data. As a result, according to energy capacities of concretes, the proportions 5% silica fume (SF) and 30% recycled aggregate are proposed as the optimum ratio.