Normal Deformation Research Articles

Buckling analysis of the porous sandwich functionally graded plates resting on Pasternak foundations by Navier solution combined with a new refined quasi-3D hyperbolic shear deformation theory

This article presents a numerical method for analyzing the compressive buckling of porous power-law functionally graded (PPFG) plates placed on Pasternak foundations, which is based on a novel refined quasi-3-dimensional hyperbolic shear deformation theory (RQHSDT) combined with the Navier solution technique. The RQHSDT employs a novel hyperbolic distribution of in-plane displacements through the plate thickness to account for non-linear variations in transverse shear stresses, satisfies the traction free boundary conditions on the top and bottom surfaces, and accounts for shear deformation and thickness stretching effects of the plates without the use of any shear correction factors. Unlike classical shear and normal deformation theories, the RQHSDT has only four variables in its displacement field, as opposed to five or more variables in other quasi-3D shear deformation theories, which reduces the number of unknown variables and governing equations in plate analyses and simplifies calculations. The governing equations of the buckling problem are derived using the virtual work principle. In problem solving, the Navier solution technique is used to obtain the exact solutions for the rectangular PPFG plates with simply supported edges subjected to in-plane loading. The accuracy of the proposed approach is confirmed by comparing the obtained results to those of previously published quasi-3D shear deformation theories. Using comprehensive parametric studies, the effects of gradient index, porosity fraction index, porosity distribution type, geometric parameters, two-direction compression ratio, and stiffness of foundation parameters on buckling of PPFG plates are investigated.

Thermoelastic bending analysis of laminated composite shells using a trigonometric shear and normal deformation theory

In the present study, a trigonometric shear and normal deformation theory using trigonometric functions in the displacement field is developed and employed for the static analysis of laminated composite spherical shells subjected to sinusoidal mechanical/thermal loads with simply supported boundary conditions. In the present theory, the effect of both transverse shear and normal strain is considered. The present theory satisfies the zero transverse shear stress conditions at the top and the bottom surfaces of the shell. By using the principle of virtual work, the governing equations and boundary conditions are derived. Navier’s solution procedure is employed to solve the governing differential equations and satisfying the boundary conditions. For validation of the present theory, obtained results are compared with higher-order theories and 3D elasticity solutions wherever possible. Thermal stresses in laminated plates are deduced from the present shell theory and compared with the exact thermoelastic solutions. Thermal stresses presented for the laminated composite spherical shells can serve as a benchmark for future work.

A Quasi-3D Higher-Order Theory for Bending of FG Nanoplates Embedded in an Elastic Medium in a Thermal Environment

This paper presents the effects of temperature and the nonlocal coefficient on the bending response of functionally graded (FG) nanoplates embedded in an elastic foundation in a thermal environment. The effects of transverse normal strain, as well as transverse shear strains, are considered where the variation of the material properties of the FG nanoplate are considered only in thickness direction. Unlike other shear and deformations theories in which the number of unknown functions is five and more, the present work uses shear and deformations theory with only four unknown functions. The four-unknown normal and shear deformations model, associated with Eringen nonlocal elasticity theory, is used to derive the equations of equilibrium utilizing the principle of virtual displacements. The effects due to nonlocal coefficient, side-to-thickness ratio, aspect ratio, normal and shear deformations, thermal load and elastic foundation parameters, as well as the gradation in FG nanoplate bending, are investigated. In addition, for validation, the results obtained from the present work are compared to ones available in the literature.

Experimental study on the shear mechanical behaviour of rock-like materials containing one embedded flaw under unloading normal stress conditions

It is difficult to cut internal defects, and capture the initiation and propagation of internal defects by direct observation in actual rocks. This article presents a new method to create internal defect samples by volatilisation of camphor. Then, in order to better understand the influence of unloading normal stress on shear mechanical behaviour, laboratory tests are carried out on rock-like samples containing one embedded penny shape flaw with constant shear stress and unloading normal stress under different stress paths and shear directions conditions. The failure pattern and fracture morphologies of rock-like samples with different shear paths, flaw inclination and shear direction are analyzed. The strength and deformation behaviour are investigated also. Results show that the degree of fracture surface of direct shear tests and linear normal unloading shear tests are smaller than that of the complex normal unloading shear tests. The normal unloading amount determines the failure mode of rock-like samples. The failure pattern transforms from tensile failure to shear failure when the normal unloading amount gradually decreases. Although normal unloading deformation plays an important role in rock failure, shear deformation has little effect on fracture mode.

A bi-potential contact formulation for recoverable adhesion between soft bodies based on the RCC interface model

An extended, ready-to-implement 3D model for quasi-industrial problems of contact with friction and recoverable interface adhesion between soft material is formulated using the Raous–Cangémi–Cocou (RCC) interface model and a bi-potential based resolution method. According to the RCC description, the recoverable adhesive interface behaviour derives from a free surface energy and a surface dissipation pseudo-potential. The obtained interface law describes both the de-bonding process of adhesive links due to tangential and normal interface deformation, and reversely, the bonding process that takes place when two surfaces approach close enough. We then propose an associated formulation coupling 3D extended interface law and Blatz–Ko hyperelastic material, that enables modelling large deformations of foam type soft matters under conditions of contact and friction with recoverable adhesion. In the end, the subsequent local contact nonlinear equations are solved using a Newton-like algorithm within the bi-potential framework. Numerical examples are performed to demonstrate the capacity of the proposed approach.

Wheel rolling on deformable ground with slippage

Wheeled vehicles can move not only on a solid supporting surface, but also on deformable surfaces (snow, ground, sand, etc.). When a pneumatic wheel with a high internal air pressure rolls over deformable soil, the nature of the wheels’ interaction with the ground is such that the wheel can be considered rigid, since its normal deformation is small. This greatly simplifies the calculations associated with the analysis of the wheeled vehicles’ operation, taking into account the transforming properties of the wheel mover, in particular, the determination of the kinematic and power parameters of the wheel. In this paper, using the method of motion reversal, the picture of physical phenomena in the contact of the wheel with the ground is considered, which made it possible to obtain relatively simple expressions for calculating the circumferential traction force and the coefficient of tangential elasticity of the “wheel - deformable ground” pair.

Numerical modelling of concrete tunnels exposed to rock fall

Tunnel entrances are among the most likely places for rock fall events. For this reason, concrete tubes are constructed before tunnel entrances against rock falls. In this study, the normal stress and the deformation in both horizontal and vertical directions occurred by crashing rock on concrete tunnel tubes were investigated using finite element method in three dimensional conditions. Different velocities and masses of falling rock analyzed to demonstrate effect of velocity on normal stress and deformations. It was observed that deformations on the concrete tube increased as the impact energy increased due to increasing velocity and mass. The mass of crashed rock, M, is changes from 3 kN to 200 kN and peak deformations could reach approximately 150 cm when the mass of falling rock was M=200 kN and V = 30 m/s. When the velocity of rock V=10 m/s just before the impact, the ratios of deformations to rock mass of 3 kN, 25 kN, and 200 kN were approximately 0.00066 m/kN, 0.0014 m/kN and 0.00175 m/kN, respectively.

Fully coupled thermo-hydro-mechanical approach to model fracture response to injection process in enhanced geothermal systems using displacement discontinuity and finite element method

Assessing, predicting, and controlling injection-induced seismicity is a major challenge for developing enhanced geothermal systems (EGS) due to the complexity of coupled thermo-hydro-mechanical (THM) processes. This study aimed to develop a fully coupled numerical model to assess the complex behavior of a low permeable matrix-fracture during non-isothermal single-phase fluid injection process. A thermo-poroelastic displacement discontinuity (DD) method combining with different forms of finite element method are implemented to encapsulate the fractured medium response and transport processes, respectively. The nonlinear characteristics of normal (changing the joint to hydraulic fracture status) and shear (changing the stick to slip fracture status) fracture deformation are taken into account through fracture constitutive relations. Developed numerical approach was applied to simulate cool water injection into fracture/matrix systems, analyzing the role of coupled processes on spatiotemporal variation of matrix-fracture stresses, temperature and pore pressure and assessing induced seismicity (slippage) and permeability alteration. Numerical simulations demonstrate a fully coupled relation between matrix dilation, shrinkage, and non-linear fracture deformation. The redistribution of dynamic and kinematic parameters along with non-linear fracture deformation showed that although the poroelastic effects are dominant in the early stages, thermoelastic effects dominate in the long-term injection stages. • A fully-coupled Thermo-Hydro-Mechanical approach was developed to model injection process in EGS. • Displacement discontinuity and finite element methods were combined to encapsulate fracture deformation and transport processes, respectively. • Fracture constitutive laws were implemented to model non-linear crack deformation. • Poroelastic effects are dominant in the early stages, and thermoelastic effects dominate in the long-term injection stages.

Flexural analysis of functionally graded sandwich plate with piezoelectric face sheet based on Lagrangian mechanics

In the present study, the static behaviour of the functionally graded material sandwich plate with the piezoelectric face sheet is analyzed. The sandwich plate comprises of FGM at its core and homogenous piezoelectric forms outer layers. The homogenous face sheets of piezoelectric materials consisting of two different types of materials viz. PZT-4 and PZT-5A. The higher order along with normal shear deformation criterias are considered as a displacement field to analyze the effect of thickness stretching on the deflection and stresses of the sandwich plate. The Lagrangian approach is implemented to derive the governing equations. The equations are solved analytically by the Navier’s method and the responses are being recorded in the form of Transverse deflection, Transverse Shear Stress and Normal Stress with varying external electrical voltages. In this study it is observed that there exists electro-mechanical coupling between FGM core and PZT face sheet. The results for the sandwich plate with FGM core and homogenous face sheets are validated with the previous studies and founds to be in good agreement. It is noted that the deflection and stresses reduces significantly with change in polarity from negative to positive.

Patient-Specific Quantification of Normal and Bicuspid Aortic Valve Leaflet Deformations from Clinically Derived Images.

The clinical benefit of patient-specific modeling of heart valve disease remains an unrealized goal, often a result of our limited understanding of the in vivo milieu. This is particularly true in assessing bicuspid aortic valve (BAV) disease, the most common cardiac congenital defect in humans, which leads to premature and severe aortic stenosis or insufficiency (AS/AI). However, assessment of BAV risk for AS/AI on a patient-specific basis is hampered by the substantial degree of anatomic and functional variations that remain largely unknown. The present study was undertaken to utilize a noninvasive computational pipeline ( https://doi.org/10.1002/cnm.3142 ) that directly yields local heart valve leaflet deformation information using patient-specific real-time three-dimensional echocardiographic imaging (rt-3DE) data. Imaging data was collected for patients with normal tricuspid aortic valve (TAV, [Formula: see text]) and those with BAV ([Formula: see text] with fused left and right coronary leaflets and [Formula: see text] with fused right and non-coronary leaflets), from which the medial surface of each leaflet was extracted. The resulting deformation analysis resulted in, for the first time, quantified differences between the in vivo functional deformations of the TAV and BAV leaflets. Our approach was able to capture the complex, heterogeneous surface deformation fields in both TAV and BAV leaflets. We were able to identify and quantify differences in stretch patterns between leaflet types, and found in particular that stretches experienced by BAV leaflets during closure differ from those of TAV leaflets in terms of both heterogeneity as well as overall magnitude. Deformation is a key parameter in the clinical assessment of valvular function, and serves as a direct means to determine regional variations in structure and function. This study is an essential step toward patient-specific assessment of BAV based on correlating leaflet deformation and AS/AI progression, as it provides a means for assessing patient-specific stretch patterns.

Coupled thermo-hydro-mechanical modelling for geothermal doublet system with 3D fractal fracture

• 3D fractal fracture existed in a geothermal doublet system. • Coupled thermo-hydro-mechanical interaction for bedrock and fracture. • Normal and shear deformations of fracture based on thin elastic layer assumption. • Evaluation of thermal breakthrough due to preferential fracture flow. The existence of preferential flow paths, such as fractures and/or fault play an vital role on the thermal breakthrough of geothermal doublet system. The interaction between the preferential flow path and bedrock is often uneven and may have typical fractal characteristic. This study proposes a thermo-hydro-mechanical coupling model considering the deformation of fractal fractures. The fractal fracture is regarded as a thin elastic layer existed in the bedrock, whoes deformation depends to the bedrock and its own mechanical properties. Subsequently, the geothermal doublet system with a three-dimensional fractal fracture is modelled and the parameters affecting thermal breakthrough are investigated numerically. Research results indicate that the thin elastic layer assumption is remarkably robust for modelling fracture opening and closing under coupling conditions. Owing to complex fracture geometry, the fracture permeability evolution presents certain heterogeneity, which is related to fractal dimension, in-situ stress, and geothermal wells layout. The cool water in fracture with larger fractal dimension can interact with the bedrock more fully and further affect the thermal breakthrough. This further suggests that the site selection of geothermal wells should consider the specific geometry of preferential flow paths to avoid premature thermal breakthrough inducing low system efficiency.

Method for the influence design assessment of a wheeled agricultural vehicle on the soil

The impact of a wheeled agricultural vehicle on the deformable support surface determines the vehicle's ability to move, as well as soil compaction, which is not desirable in agriculture. The agricultural machine must not cause more pressure on the ground than is permissible. Therefore, in the tasks of design numerical modelling of the agricultural vehicle movement or trailer, it is required to calculate the specified parameter. It is impossible to calculate without knowledge of the geometric characteristics of the contact spot associated with the normal deformation of the tire under normal load. To calculate these characteristics, it is necessary to have universal dependencies for determining the normal stiffness of the tire. These are available for tires of various purposes. The elastic properties of ultra-low pressure tires are insufficiently studied. Experimental studies of the elastic properties of these tires have been carried out with the authors participation. However, there are currently no dependencies to describe them. This does not provide the possibility of a correct design calculation of the influence of such tires on the soil. The purpose of the work: to develop a universal method for calculating the influence on the soil of agricultural vehicle. A universal method for calculating the impact of a wheeled agricultural machine on the ground has been developed. Universal design-experimental dependence for determining the normal stiffness of ultra-low pressure tires is obtained. It takes into account tire pressure, normal load under specific conditions and geometric characteristics.

Railway Track Stress–Strain Analysis Using High-Precision Accelerometers

We propose a new approach for railway path diagnostics on the basis of track line stress–strain analysis using the data provided by high-precision accelerometers. This type of sensor provides sufficient accuracy with lower costs, and enables the development of a railway digital twin, according to the concept of the Internet of Things. The installation of sensors on a railway track along its entire length allows real-time monitoring of the states of the technical parameters of the railway track, and using mathematical methods to evaluate its wear on the basis of constantly received data. This paper presents an original 3D model of a railway track line and the results of its analysis using a finite element method. To test the model, we performed an analysis of the normal stresses and deformations in the elements of a railway track by simulating the impact of rolling stock on a section of a railway track with intermediate rail fastenings, ZhBR-65SH. The research results were probated and tested at the testing ground of the Kuibyshev branch of Russian Railways, the Samara track. The proposed approach makes it possible to determine the load of the track, and knowing the movement of the rail, to calculate the structural stress in the elements of the railway track, to constantly monitor the parameters of the slope and rail subsidence.

Research on Shear Behavior of Sand–Structure Interface Based on Monotonic and Cyclic Tests

In order to study the shear behavior of the interface between sand and structure, a series of shear tests were carried out using an HJ-1 ring shear apparatus (Nanjing, China). First, through the monotonic shear tests, the loose sand and dense sand were sheared at the steel interface with different roughnesses. The results showed that when the interface was relatively smooth, the shear stress–shear displacement curves of loose sand and dense sand both exhibit strain hardening characteristics. When the interface was rough, the dense sand showed strain softening. The initial shear stiffness of the sand–steel interface increased with the increase in normal stress, interface roughness, or sand relative density. Then, considering the influence of initial shear stress, through the cyclic shear test, this work analyzed the shape of the loading and unloading curves and the development law of cumulative normal deformation, and discussed the change of loading and unloading shear stiffness under different stress level amplitudes and the residual deformation generated during the cycle. The research results showed that loose sand and dense sand generally shrunk in volume during the cycle. The initial loading process was similar to the case of static loading. In the later dynamic loading process, the shear shrinkage per cycle was relatively small and continued to develop. Additionally, it was found that the unloading stiffness of the sand–steel interface is always greater than the initial loading stiffness. As the number of cycles increases, the loading stiffness increases, and it may eventually approach the unloading stiffness.

Study of a lightweight self-adaptation multi-morphing skin inspired by mechanics of epidermis cell walls producing the leaf’s unique smooth shape

Inspired by mechanics of epidermis cell walls in the forming process of the unique smooth shape of a leaf, the constitutive model of an out-of-plane compressive sandwich panel consisting of outer skins and a biomimetic Isosceles Trapezoid Corrugated Lattice Cellular (bio-ITCLC) core is built by theory and experiment to provide guidance for meeting structural requirements of a skin with the self-adaptation multi-morphing application. This above constitutive model shows that by decreasing the skin’s tangential stiffness and simultaneously increasing the bio-ITCLC core’s vertical stiffness can use less weight to decouple the mutual suppression between high tangential and low normal deformations of the skin. Besides, one proposed optimal design for a self-adaptation multi-morphing skin is that the skin comprising of a flexible matrix modified by curvilinear fibres is supported by the bio-ITCLC core with self-adjusting anisotropy stiffness according to new circumstances. And this dynamic self-adjusting anisotropy stiffness follows such a rule that the transverse stiffness along the y-axis or vertical stiffness along the z-axis is increased while the transverse stiffness along the x-axis is decreased.

Investigation of the Shear Mechanical Behavior of Sandstone with Unloading Normal Stress after Freezing–Thawing Cycles

Freezing–thawing action has a great impact on the physical and mechanical deterioration processes of rock materials in cold areas where environmental changes are very complicated. The direct shear test under unloading normal stress was adopted to investigate the shear mechanical behavior of sandstone samples after a freezing–thawing cycle in this paper. The failure shear displacement (Dsf), the failure normal displacement (Dnf), the shear displacement of unloading (Dsu), and the normal displacement of unloading (Dnu) were analyzed to describe the evolution of shear and normal deformation during the test. The results indicated that the shear displacement increased as the freezing–thawing cycle duration increased in a direct shear test under unloading normal stress. The unloading rate and the number of freezing–thawing cycles affected the failure pattern of the rock sample significantly in both the direct shear test under unloading normal stress and the direct shear test. The three-dimensional inclination angle, the distortion coefficient, and the roughness correlation coefficient of the fracture surface are dependent on the number of freezing–thawing cycles and the unloading rate. The surface average gradient mode of the fracture surface decreased as the freezing–thawing cycle times and unloading rate rose.

TOOTH CONTACT ANALYSIS OF A DESIGNED PLANETARY GEAR DRIVE FOR THE VEHICLE INDUSTRY

A planetary gear drive consists of a sun gear, planet pinions and an internal gear. We designed a complex gear system which is usable in the field of the vehicle industry into the automatized robots. The system was designed by GearTeq software which is connected with the SolidWorks designer software. After the assembly and the motion simulations tooth contact analysis (TCA) was made to analyse the normal stresses and the normal deformations on the connecting surface of the planet pinions and the internal gear by different load moments.

Calculating the attenuation of stress waves passing through an in situ stressed joint using a double nonlinear model

In situ stress is a significant characteristic of underground rock masses. In this work, based on the time-domain recursive method (TDRM), a new theoretical approach is proposed to study the oblique propagation of an S-wave across an in situ stressed joint wherein the normal and shear deformations are both treated nonlinearly. Equations are first established for the propagation of stress waves across a rock mass subjected to a combination of gravitational and tectonic stress. The veracity of the wave propagation equations is then investigated by comparing our theoretical results with those obtained using the Universal Distinct Element Code (UDEC). A comparison of the waveforms predicted using the continuously yielding and existing models is also presented to investigate their differences. Finally, parametric studies are conducted to investigate the effects of joint angle, in situ stress, lateral pressure coefficient, and incident wave amplitude on the propagation of the wave. The results show that the effect of in situ stress on wave propagation is related to the joint angle and lateral pressure coefficient because these factors decide the initial stress and contact states of the joint.

Anti-sway method for reducing vibrations on a tower crane structure

Abstract We develop a solution to the problem of the behavior of a tower crane considered as a deformable system, and therefore subject to vibrations, whereas the controlled movement of a payload is implemented. The motion of the payload is calculated taking into account the normal vibration modes of the tower crane and the swaying of the payload. A “command smoothing” method relative to an open-loop system is used for reducing the sway of the payload, through smoothing the original command by the crane operator. This leads, as a consequence, to a reduction in the vibrations of the crane structure. An iterative calculation of the sway angle and the corresponding applied velocity profiles as input to the crane motors is applied. The tower crane is considered as a high nonlinear underactuated system; it is modeled considering the possible deformation of the structure. The results relating to the normal deformations of the crane are obtained, highlighting how these vibrations are strongly attenuated when an anti-sway system for the payload is implemented. Therefore, it is shown how this control leads to the best results in terms of performance for both the payload movement (shortest possible profile for the rotation movement and damping of the load oscillation) and the structure of the tower crane. Applying the method described in this paper, the structure of the tower crane does not undergo the strong horizontal and vertical oscillations that occur when the elastic structure is not considered in the crane model.

Toward a Comprehensive Delineation of White Matter Tract-Related Deformation.

Finite element (FE) models of the human head are valuable instruments to explore the mechanobiological pathway from external loading, localized brain response, and resultant injury risks. The injury predictability of these models depends on the use of effective criteria as injury predictors. The FE-derived normal deformation along white matter (WM) fiber tracts (i.e., tract-oriented strain) recently has been suggested as an appropriate predictor for axonal injury. However, the tract-oriented strain only represents a partial depiction of the WM fiber tract deformation. A comprehensive delineation of tract-related deformation may improve the injury predictability of the FE head model by delivering new tract-related criteria as injury predictors. Thus, the present study performed a theoretical strain analysis to comprehensively characterize the WM fiber tract deformation by relating the strain tensor of the WM element to its embedded fiber tract. Three new tract-related strains with exact analytical solutions were proposed, measuring the normal deformation perpendicular to the fiber tracts (i.e., tract-perpendicular strain), and shear deformation along and perpendicular to the fiber tracts (i.e., axial-shear strain and lateral-shear strain, respectively). The injury predictability of these three newly proposed strain peaks along with the previously used tract-oriented strain peak and maximum principal strain (MPS) were evaluated by simulating 151 impacts with known outcome (concussion or non-concussion). The results preliminarily showed that four tract-related strain peaks exhibited superior performance than MPS in discriminating concussion and non-concussion cases. This study presents a comprehensive quantification of WM tract-related deformation and advocates the use of orientation-dependent strains as criteria for injury prediction, which may ultimately contribute to an advanced mechanobiological understanding and enhanced computational predictability of brain injury.