A novel formulation of material nonlinear analysis in structural mechanics

This article demonstrates a novel approach for material nonlinear analysis.This analysis procedure eliminates tedious and lengthy step by step incremental and then iterative procedure adopted classically and gives direct results in the linear as well as in nonlinear range of the material behavior.Use of elastic moduli is eliminated.Instead,stress and strain functions are used as the material input in the analysis procedure.These stress and strain functions are directly derived from the stress-strain behavior of the material by the method of curve fitting.This way,the whole stress-strain diagram is utilized in the analysis which naturally exposes the response of structure when loading is in nonlinear range of the material behavior.It is found that it is an excellent computational procedure adopted so far for material nonlinear analysis which gives very accurate results,easy to adopt and simple in calculations.The method eliminates all types of linearity assumptions in basic derivations of equations and hence,eliminates all types of possibility of errors in the analysis procedure as well.As it is required to know stress distribution in the structural body by proper modelling and structural idealization,the proposed analysis approach can be regarded as stress-based analysis procedure.Basic problems such as uniaxial problem,beam bending,and torsion problems are solved.It is found that approach is very suitable for solving the problems of fracture mechanics.Energy release rate for plate with center crack and double cantilever beam specimen is also evaluated.The approach solves the fracture problem with relative ease in strength of material style calculations.For all problems,results are compared with the classical displacement-based liner theory.

Artificial Neural Network Methods for the Solution of Second Order Boundary Value Problems

We present a method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy.In this procedure,a coarse grid of training points is used at the initial training stages,while more points are added at later stages based on the value of the residual at a larger set of evaluation points.This method increases the robustness of the neural network approximation and can result in significant computational savings,particularly when the solution is non-smooth.Numerical results are presented for benchmark problems for scalar-valued PDEs,namely Poisson and Helmholtz equations,as well as for an inverse acoustics problem.

Oblique perforation of thick metallic plates by rigid projectiles

Oblique perforation of thick metallic plates by rigid projectiles with various nose shapes is studied in this paper. Two perforation mechanisms, i.e., the hole enlargement for a sharp projectile nose and the plugging formation for a blunt projectile nose, are considered in the proposed analytical model. It is shown that the perforation of a thick plate is dominated by several non-dimensional numbers, i.e., the impact function, the geometry function of projectile, the non-dimensional thickness of target and the impact obliquity. Explicit formulae are obtained to predict the ballistic limit, residual velocity and directional change for the oblique perforation of thick metallic plates. The proposed model is able to predict the critical condition for the occurrence of ricochet. The proposed model is validated by comparing the predictions with other existing models and independent experimental data.

Bifurcation and buckling analysis of a unilaterally confined self-rotating cantilever beam

A nonlinear dynamic model of a simple nonholonomic system comprising a self-rotating cantilever beam subjected to a unilateral locked or unlocked constraint is established by employing the general Hamilton＇s Variational Principle. The critical values, at which the trivial equilibrium loses its stability or the unilateral constraint is activated or a saddle-node bifurcation occurs, and the equilibria are investigated by approximately analytical and numerical methods. The results indicate that both the buckled equilibria and the bifurcation mode of the beam are different depending on whether the distance of the clearance of unilateral constraint equals zero or not and whether the unilateral constraint is locked or not. The unidirectional snap-through phenomenon （i.e. catastrophe phenomenon） is destined to occur in the system no matter whether the constraint is lockable or not. The saddle-node bifurcation can occur only on the condition that the unilateral constraint is lockable and its clearance is nonzero. The results obtained by two methods are consistent.

FE modeling of concrete beams and columns reinforced with FRP composites

Compression and flexure members such as columns and beams are critical in a structure as its failure could lead to the collapse of the structure.In the present work,numerical analysis of square and circle short columns,and reinforced concrete(RC)beams reinforced with fiber reinforced polymer composites are carried out.This work is divided into two parts.In the first part,numerical study of axial behavior of square and circular concrete columns reinforced with Glass Fiber Reinforced Polymer(GFRP)and Basalt Fiber Reinforced Polymer(BFRP)bars and spiral,and Carbon Fiber Reinforced Polymer(CFRP)wraps is conducted.The results of the first part showed that the axial capacity of the circular RC columns reinforced with GFRP increases with the increase of the longitudinal reinforcement ratio.In addition,the results of the numerical analysis showed good correlation with the experimental ones.An interaction diagram for BFRP RC columns is also developed with considering various eccentricities.The results of numerical modeling of RC columns strengthened with CFRP wraps revealed that the number and the spacing between the CFRP wraps provide different levels of ductility enhancement to the column.For the cases considered in this study,column with two middle closely spaced CFRP wraps demonstrated the best performance.In the second part of this research,flexural behavior of RC beams reinforced with BFRP,GFRP and CFRP bars is investigated along with validation of the numerical model with the experimental tests.The results resembled the experimental observations that indicate significant effect of the FRP bar diameter and type ont he flexural capacity of the RC beams.It was also shown that Increasing the number of bars while keeping the same reinforcement ratio enhanced the stiffness of the RC beam.

Modeling of Normal Perforation of Reinforced Concrete Slabs by a Rigid Projectile

An analytical model on the normal perforation of reinforced concrete slabs is constructed. The effect of reinforcing bars is further hybridized in a general three-stage model consisting of initial cratering, tunnelling and shear plugging. Besides three dimensionless numbers, i. e., the impact function I, the geometry function of projectile N and the dimensionless thickness of concrete target X, which are employed to predict the ballistic performance of perforation of concrete slabs, the reinforcement ratio Ps of concrete and the tensile strength fs of reinforcing bars are considered as the other main factors influencing the perforation process. Simpler solutions of ballistic performances of normal perforation of reinforced concrete slabs are formulated. Theoretical predictions agree well with individual published experimental data.

Semi-theoretical analyses of the concrete plate perforated by a rigid projectile

Based on the three-stage perforation model, a semi-theoretical analysis is conducted for the ballistic per- formances of a rigid kinetic projectile impacting on concrete plates. By introducing the projectile resistance coefficients, dimensionless formulae are proposed for depth of penetra- tion （DOP）, perforation limit thickness, ballistic limit veloc- ity, residual velocity and perforation ratio, with the projec- tile nosed geometries and projectile-target interfacial fric- tion taken into account. Based on the proposed formula for DOP and lots of penetration tests data of normal and high strength concrete targets, a new expression is obtained for target strength parameter. By comparisons between the re- sults of the proposed formulae and existing empirical formu- lae and large amount of projectile penetration or perforation tests data for monolithic and segmented concrete targets, the validations of the proposed formulae are verified. It is found that the projectile-target interfacial friction can be neglected in the predictions of characteristic ballistic parameters. The dimensionless DOP for low-to-mid speed impacts of non-flat nosed projectiles increases almost linearly with the impact factor by a coefficient of 2/（nS）. The anti-perforation ability of the multilayered concrete plates is dependent on both the target plate thickness and the projectile impact velocity. The variation range of the perforation ratio is 1-3.5 for concrete targets.

Mechanical properties of 3D carbon/carbon composites by nanoindentation technique

Nanoindentation tests were conducted to investigate the near-surface mechanical properties of the individual components(fiber and matrix) for three-dimensional reinforced carbon/carbon composites(3D C/C).Optical microscope and polarizing light microscope were used to characterize the microstructure of 3D C/C.The microscopy results show that large number of pores and cracks exist at both bundle/matrix interface and pitch carbon matrix.These defects have important effect on the mechanical behavior of 3D C/C.The in situ properties for components of 3D C/C were acquired by nanoindentation technique.Relative to the matrix sample,the fiber samples have more larger values for modulus,stiffness and hardness.However,there is no significant difference of modulus and stiffness among fiber samples with different directions.

MODAL TEST AND ANALYSIS OF CANTILEVER BEAM WITH TIP MASS

The phenomenon of dynamic stiffening is a research field of general interest for flexible multi-body systems.In fact,there are not only dynamic stiffening but also dynamic softening phenomenon in the flexible multi-body systems.In this paper,a non-linear dynamic model and its linearization characteristic equations of a cantilever beam with tip mass in the centrifugal field are established by adopting the general Hamilton Variational Principle.Then,the problems of the dynamic stiffening and the dynamic softening are studied by using numerical simulations.Meanwhile, the modal test is carried out on our centrifuge.The numerical results show that the system stiffness will be strengthened when the centrifugal tension force acts on the beam (i.e.the dynamic stiffening).However,the system stiffness will be weakened when the centrifugal compression force acts on the beam (i.e.the dynamic softening). Furthermore,the equilibrium position of the system will lose its stability when the inertial force reaches a critical value.Through theoretical analysis,we find that this phenomenon comes from the effect of dynamic softening resulting from the centrifugal compression force.Our test results verify the above conclusions and confirm that both dynamic stiffening and softening phenomena exist in flexible multi-body systems.

Three-Dimensional Isogeometric Analysis of Flexoelectricity with MATLAB Implementation

Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa.The truncated pyramid compression test is among the most common setups to estimate the flexoelectric effect.We present a three-dimensional isogeometric formulation of flexoelectricity with its MATLAB implementation for a truncated pyramid setup.Besides educational purposes,this paper presents a precise computational model to illustrate how the localization of strain gradients around pyramidal boundary shapes contributes in generation of electrical energy.The MATLAB code is supposed to help learners in the Isogeometric Analysis and Finite Elements Methods community to learn how to solve a fully coupled problem,which requires higher order approximations,numerically.The complete MATLAB code which is available as source code distributed under a BSD-style license,is provided in the part of Supplementary Materials of the paper.

Elastoplastic model for discontinuous shear deformation of deep rock mass

Deep rock mass possesses some unusual properties due to high earth stress,which further result in new problems that have not been well understood and explained up to date.In order to investigate the deformation mechanism,the complete deformation process of deep rock mass,with a great emphasis on local shear deformation stage,was analyzed in detail.The quasi continuous shear deformation of the deep rock mass is described by a combination of smooth functions:the averaged distribution of the original deformation field,and the local discontinuities along the slip lines.Hence,an elasto-plastic model is established for the shear deformation process,in which the rotational displacement is taken into account as well as the translational component.Numerical analysis method was developed for case study.Deformation process of a tunnel under high earth stress was investigated for verification.

Parametric study on mass loss of penetrators

Earth penetration weapon （EPW） is applicable for attacking underground targets protected by reinforced concrete and rocks. With increasing impact velocity, the mass loss/abrasion of penetrator increases, which significandy decreases the penetration efficiency due to the change of nose shape. The abrasion may induce instability of the penetrator, and lead to failure of its structure. A common disadvantage, i.e. dependence on corresponding experimen- tal results, exists in all the available formulae, which limits their ranges of application in estimating the mass loss of penetrator. In this paper, we conduct a parametric study on the mass loss of penetrator, and indicate that the mass loss of penetrator can be determined by seven variables, i.e., the initial impact velocity, initial nose shape, melting heat, shank diameter of projectile and density and strength of target as well as the aggregate hardness of target. Further discussion on factors dominant in the mass abrasion of penetrator are given, which may be helpful for optimizing the target or the projectile for defensive or offensive objectives, respectively.

Nonlinear flutter of a two-dimension thin plate subjected to aerodynamic heating by differential quadrature method

The problem of nonlinear aerothermoelasticity of a two-dimension thin plate in supersonic airflow is examined. The strain-displacement relation of the von Karman＇s large deflection theory is employed to describe the geometric non-linearity and the aerodynamic piston theory is employed to account for the effects of the aerodynamic force. A new method, the differential quadrature method （DQM）, is used to obtain the discrete form of the motion equations. Then the Runge-Kutta numerical method is applied to solve the nonlinear equations and the nonlinear response of the plate is obtained numerically. The results indicate that due to the aerodynamic heating, the plate stability is degenerated, and in a specific region of system parameters the chaos motion occurs, and the route to chaos motion is via doubling-period bifurcations.

Experimental Research on Behavior of Composite Material Projectile Penetrating Concrete Target

Projectile made of carbon fiber composite material shell and metal warhead penetrates concrete target at speeds of 336,m/s,447,m/s and 517,m/s.The angles between the perpendicu-lar of target surface and projectile axis are 0°and 30°.The thickness of concrete target is 200,mm and the compression strength is 30 MPa.The experimental results indicate that the strength of composite material structure is high.Composite projectile can go through concrete tar-get without fiber segregation and breakage.The percent fill is 18.5% in the composite material projectile.It is about twice as that of metal projectile,if the density of metal is taken as 7.8,g/cm3.Comparing with metal projectile,low-density,high-strength composite material can lessen projec-tile weight,improve charge-weight ratio of detonator and enhance destructive powder.

Damage modeling of ballistic penetration and impact behavior of concrete panel under low and high velocities

This work presents a numerical simulation of ballistic penetration and high velocity impact behavior of plain and reinforced concrete panels.This paper is divided into two parts.The first part consists of numerical modeling of reinforced concrete panel penetrated with a spherical projectile using concrete damage plasticity(CDP)model,while the second part focuses on the comparison of CDP model and Johnson-Holmquist-2(JH-2)damage model and their ability to describe the behavior of concrete panel under impact loads.The first and second concrete panels have dimensions of 1500 mm1500 mm150 mm and 675 mm675 mm200 mm,respectively,and are meshed using 8-node hexahedron solid elements.The impact object used in the first part is a spherical projectile of 150 mm diameter,while in the second part steel projectile of a length of 152 mm is modeled as rigid element.Failure and scabbing characteristics are studied in the first part.In the second part,the comparison results are presented as damage contours,kinetic energy of projectile and internal energy of the concrete.The results revealed a severe fracture of the panel and high kinetic energy of the projectile using CDP model comparing to the JH-2 model.In addition,the internal energy of concrete using CDP model was found to be less comparing to the JH-2 model.

Multiphase Equation of States of the Solid and Liquid Phases of Al and Ta

The multiphase equation of states (EOSs) of both the solid and liquid phases of Al and Ta are presented.These EOSs are carried out on the basis of the Helmholtz free energy,where the ion vibration free energy is evaluated from the mean field potential (MFP) model we recently proposed [Physica B 406 (2011)4163].The calculated results show that our multiphase EOSs can give a good reproduction of the measured phase diagrams and other experimental data,including static high-pressure measurements,shock Hugoniots and the thermodynamic quantities of these metals.

Applying ANN,ANFIS and LSSVM Models for Estimation of Acid Solvent Solubility in Supercritical CO_(2)

In the present work,a novel machine learning computational investigation is carried out to accurately predict the solubility of different acids in supercritical carbon dioxide.Four different machine learning algorithms of radial basis function,multi-layer perceptron(MLP),artificial neural networks(ANN),least squares support vector machine(LSSVM)and adaptive neuro-fuzzy inference system(ANFIS)are used to model the solubility of different acids in carbon dioxide based on the temperature,pressure,hydrogen number,carbon number,molecular weight,and the dissociation constant of acid.To evaluate the proposed models,different graphical and statistical analyses,along with novel sensitivity analysis,are carried out.The present study proposes an efficient tool for acid solubility estimation in supercritical carbon dioxide,which can be highly beneficial for engineers and chemists to predict operational conditions in industries.

MECHANICAL BEHAVIOR OF FCC CRYSTAL SIMULATED BY 3-D DISCRETE DISLOCATION DYNAMICS

To simulate the mechanical behavior of the FCC crystal with the lower Peierls stress, the stiff property and physical meaning of the differential equation group consisting of dislocation evolution and mechanical state was investigated based on the 3-D discrete dislocation dynamics; the results indicate that the differential equation group is serious stiff, namely the external stress changes more quickly than dislocation evolution. Using the established numerical algorithm, the mechanical behavior of FCC crystal was simulated with the dislocations located in the parallel slip planes, and the effect of strain rate on the dislocation configuration and mechanical behavior, and the sat- uration process of mobile dislocation were discussed. The simulation results indicate that the numerical algorithm can efficiently simulate the dislocation dipole and the low strain rate loading.

Comparison Among Depths of Penetration of Different Targets Subjected to Rigid Projectile Impact

The ratios of depth of penetration (DOP) of different targets under the same penetration condition was investigated according to the dimensionless formula of DOP of different targets penetrated by a non-deformable projectile.Results show that various targets may be equivalent to each other.The applicable range of the equivalence and the feasibility of targets substitution were discussed by integrating the available test data.

Forecasting Damage Mechanics By Deep Learning

We in this paper exploit time series algorithm based deep learning in forecasting damage mechanics problems.The methodologies that are able to work accurately for less computational and resolving attempts are a significant demand nowadays.Relied on learning an amount of information from given data,the long short-term memory(LSTM)method and multi-layer neural networks(MNN)method are applied to predict solutions.Numerical examples are implemented for predicting fracture growth rates of L-shape concrete specimen under load ratio,single-edge-notched beam forced by 4-point shear and hydraulic fracturing in permeable porous media problems such as storage-toughness fracture regime and fracture-height growth in Marcellus shale.The predicted results by deep learning algorithms are well-agreed with experimental data.