Elastic Displacement Research Articles

Performance-Based Design Method of Hinged Wall with Buckling-Restrained Braces at Base Using the Elastic Displacement Spectrum

A performance-based seismic design method using the elastic displacement design spectrum based on equal displacement approximation is proposed for the Hinged Wall with BRBs at Base (HWBB) structural system. HWBB is simplified as an Equivalent Single Degree of Freedom (ESDOF) system. Design flowcharts are given. The proposed design approach aims to limit the lateral displacements to an allowable target displacement. Design examples are presented and target displacements are compared with numerical results. The results indicate that the plastic response of the HWBB structural system is accurately predicted by the elastic displacement spectrum, which verified that the performance-based design method of HWBB is accurate.

Factors Influencing Radiation Sound Fields in Logging While Drilling Using an Acoustic Dipole Source

With the increasing number of complex well types in the development stage of oil and gas fields, it is becoming increasingly urgent to use remote detection logging while drilling (LWD) to explore the geological structures in a formation. In this paper, the feasibility and reliability of the dipole remote detection of logging while drilling are demonstrated theoretically. For this purpose, we use an asymptotic solution of elastic wave far-field displacement to derive the calculation formula for the radiation pattern and energy flux of an LWD dipole source. The effects of influencing factors, including the source frequency, formation property, drill collar size, and mud parameter, on the radiation pattern and energy flux are analyzed. The results show that the horizontally polarized shear wave (SH-wave) has a greater advantage in imaging the reflector compared with the cases of the compressive wave (P-wave) and vertically polarized shear wave (SV-wave), which indicates the dominance of the SH-wave in dipole remote detection while drilling. The optimal source excitation frequency of 2.5 kHz and inner and outer radii of the drill collar of 0.02 and 0.1 m, respectively, should be considered in the design of an LWD dipole shear wave reflection tool. However, the heavy drilling mud is not conducive to remote detection during logging while drilling. In addition, the reflection of the SH-wave for the LWD condition is simulated. Under the conditions of optimal source frequency, drill collar size, and mud parameters, the reflection of the SH-wave signal is still detected under the fast formation.

Failure analysis and structural optimization of unequal-parameter metal bellows in resistance to bending and torsional composite deformation

In practical engineering applications, metal bellows are subjected to complex environmental conditions, and they usually deform under the combined effects of tension, bending and torsion. In this paper, the bending and torsion composite deformation of unequal parameter metal bellows arranged alternately by large wave and wavelet is studied. Firstly, the finite element model of metal bellows is constructed, and the finite element simulation analysis of its mechanical properties is carried out. Taking the simulation results as samples, the multi-objective structural optimization of unequal parameter metal bellows under the condition of bending and torsion composite deformation is carried out. Combined with the bending-torsion composite deformation test and fracture microscopic characterization, the bending-torsion composite deformation characteristics and fracture failure mechanism of equal-parameter metal bellows (EPMB) and unequal-parameter metal bellows (Un-EPMB) were compared and analyzed. The results show that under the same deformation conditions, compared with the EPMB, the elastic limit bending line displacement and elastic limit torsion angle displacement of Un-EPMB are increased by 52.94 %, and the bending and torsional stiffness are greatly improved, moreover, the alternating waveform arrangement led to relatively gradual stress transfer through the Un-EPMB during the bending-torsion composite deformation process, thereby reducing stress concentration. Thus, the Un-EPMB exhibited more favorable mechanical properties. Unlike in the EPMB, which underwent fracture along the grain boundary, the cracks in the Un-EPMB appeared in the middle layer and propagated to both sides in a wavelike pattern. The dimples were distributed in the middle layer of the fracture, which indicates ductile behavior.

On an isotropic porous solid cylinder: the analytical solution and sensitivity analysis of the pressure

Within this work, we perform a sensitivity analysis to determine the influence of the material input parameters on the pressure in an isotropic porous solid cylinder. We provide a step-by-step guide to obtain the analytical solution for a porous isotropic elastic cylinder in terms of the pressure, stresses, and elastic displacement. We obtain the solution by performing a Laplace transform on the governing equations, which are those of Biot’s poroelasticity in cylindrical polar coordinates. We enforce radial boundary conditions and obtain the solution in the Laplace transformed domain before reverting back to the time domain. The sensitivity analysis is then carried out, considering only the derived pressure solution. This analysis finds that the time t, Biot’s modulus M, and Poisson’s ratio v have the highest influence on the pressure whereas the initial value of pressure P0 plays a very little role.

Study on the creep crack growth testing of metals based on direct and indirect methods

Research on creep crack growth in defective materials or structures at high temperatures is essential for structural security evaluations. As the creep displacement rates of the specimens are estimated using the stress intensity factor KI and plastic J-integral JP, the traditional ASTM method is essentially an indirect method and some limitations have been discovered in previous studies. Based on the quasi-static load–displacement and creep displacement rate models for specimens with mode-I crack, an indirect method for creep crack growth testing is proposed according to the derived formula of elastic and plastic displacement rate and a direct method that obtains the creep crack growth rate of materials using only the crack length a. Furthermore, an iterative method for obtaining the real-time crack length through displacement–time curves was discussed by combining the indirect and direct methods. The proposed methods were verified using the results of finite element analysis (FEA) and experimental results for various materials. These results show that the direct method for creep crack growth testing is simpler and more effective than the indirect method, and the results predicted by the new methods are consistent with those obtained using traditional and literature-based methods.

An Assessment of the Mechanical Deformation Behavior of Three Different Clear Aligner Materials: A Digital Image Correlation Analysis

Introduction: The present study aimed to investigate the deformation behavior of three different clear aligner systems, CA® Pro+ Clear Aligner (Scheu Dental, Iserlohn, Germany), Taglus Premium (Taglus Company, Mumbai, India), and Spark Trugen (Ormco Corp., Orange, CA, USA), under compression testing, using the digital image correlation (DIC) technique. Materials and Methods: A total of 15 patients were treated with each of the three aligner systems, resulting in 45 sets of aligners. Each aligner set was fixed on the 3D-printed dental arches and then in an articulator. Then, the samples were subjected to occlusal forces using a purpose-built test stand to allow for controlled force application and precise displacement determination. The DIC technique was used for capturing the deformation behavior, providing detailed strain and displacement fields. Statistical analysis was performed using one-way ANOVA and Bonferroni post hoc tests with a significance of 0.05. Results: The results indicate that the Spark system exhibited the most substantial rigid displacement. Furthermore, the elastic deformation values of the Spark and Taglus systems were significantly higher than those of the CA Pro+ system (p > 0.05). Conclusions: The Spark Trugen clear aligner system demonstrated a lower stability to rigid displacement and elastic deformation under compression testing compared to the Scheu CA® Pro+ Clear Aligner and Taglus Premium. All three tested clear aligner systems showed an increased resistance to elastic displacement and rigid deformation in the mandibular arch.

A quadratic optimization program for the inverse elastography problem

In this work we focus on the development of a numerical algorithm for the inverse elastography problem. The goal is to perform an efficient material parameter identification knowing the elastic displacement field induced by a mechanical load. We propose to define the inverse problem through a quadratic optimization program which uses the direct problem formulation to define the objective function. In this way, we end up with a convex minimization problem which attains its minimum at the solution of a linear system. The effectiveness of our method is illustrated through numeral examples.

Analysis of the periodicity of movements of mechanisms with elastic links of variable length

Abstract Elastic dynamic systems with open kinematic chains are effectively described by a recursive model of the generalized Newton–Euler method with the provision of computational algorithms with a degree of complexity proportional to the dimension of these systems, i.e. O(n). Such systems, in particular, are elastic manipulators, some of which are discussed in this article. In the case when elastic dynamical systems have closed kinematic circuits, the application of a numerical analysis strategy without reversing the mass matrix is extremely difficult. The analysis of the simplest type of elastic mechanisms with closed circuits, such as a crank–slide mechanism and a four–pin mechanism with elastic connecting rods, revealed a peculiar picture of the periodicity of the functions of elastic movements of connecting rods, which differs significantly from the periods of operation of the mechanisms themselves. In this article, the properties of the periodicity (or pseudo-periodicity) of the elastic displacement function of mechanisms with elastic links of variable length are investigated using examples of numerical dynamic analysis of crank–rocker mechanisms.

Nanoindentation Creep Behavior of Additively Manufactured H13 Steel by Utilizing Selective Laser Melting Technology.

Nowadays, H13 hot work steel is a commonly used hot work die material in the industry; however, its creep behavior for additively manufactured H13 steel parts has not been widely investigated. This research paper examines the impact of volumetric energy density (VED), a critical parameter in additive manufacturing (AM), and the effect of post heat-treatment nitrification on the creep behavior of H13 hot work tool steel, which is constructed through selective laser melting (SLM), which is a powder bed fusion process according to ISO/ASTM 52900:2021. The study utilizes nanoindentation tests to investigate the creep response and the associated parameters such as the steady-state creep strain rate. Measurements and observations taken during the holding phase offer a valuable understanding of the behavior of the studied material. The findings of this study highlight a substantial influence of both VED and nitrification on several factors including hardness, modulus of elasticity, indentation depth, and creep displacement. Interestingly, the creep strain rate appears to be largely unaltered by these parameters. The study concludes with the observation that the creep stress exponent (n) shows a decreasing trend with an increase in VED and the application of nitrification treatment.

Synchrotron-based x-ray diffraction analysis of energetic ion-induced strain in GaAs and 4H-SiC

Strain engineering using ion beams is a current topic of research interest in semiconductor materials. Synchrotron-based high-resolution x-ray diffraction has been utilized for strain-depth analysis in GaAs irradiated with 300 keV Ar and 4H-SiC and GaAs irradiated with 100 MeV Ag ions. The direct displacement-related defect formation, anticipated from the elastic energy loss of Ar ions, can well explain the irradiation-induced strain depth profiles. The maximum strain in GaAs is evaluated to be 0.88% after Ar irradiation. The unique energy loss depth profile of 100 MeV Ag (swift heavy ions; SHIs) and resistance of pristine 4H-SiC and GaAs to form amorphous/highly disordered ion tracks by ionization energy loss of monatomic ions allow us to examine strain buildup due to the concentrated displacement damage by the elastic energy loss near the end of ion range (∼12 μm). Interestingly, for the case of SHIs, the strain-depth evolution requires consideration of recovery by ionization energy loss component in addition to the elastic displacement damage. For GaAs, strain builds up throughout the ion range, and the maximum strain increases and then saturates at 0.37% above an ion fluence of 3×1013 Ag/cm2. For 4H-SiC, the maximum strain reaches 4.6% and then starts to recover for fluences above 1×1013 Ag/cm2. Finally, the contribution of irradiation defects and the purely mechanical contribution to the total strain have been considered to understand the response of different compounds to ion irradiation.

Towards to Theory of the X-ray Diffraction Tomography of Crystals with Nano-Sized Defects

X-ray diffraction tomography is an innovative method that is widely used to obtain 2D-phase-contrast diffraction images and their subsequent 3D-reconstruction of structural defects in crystals. The most frequent objects of research are linear and helical dislocations in a crystal, for which plane wave diffraction images are the most informative, since they do not contain additional interference artifacts unrelated to the images of the defects themselves. In this work the results of modeling and analysis of 2D plane wave diffraction images of a nano-dimensional Coulomb-type defect in a Si(111) thin crystal are presented based on the construction of numerical solutions of the dynamic Takagi-Taupin equations. An adapted physical expression for the elastic displacement field of the point defect, which excludes singularity at the defect location in the crystal, is used. A criterion for evaluating the accuracy of numerical solutions of the Takagi-Taupin equations is proposed and used in calculations. It is shown that in the case of the Coulomb-type defect elastic displacement field, out of the two difference algorithms for solving the Takagi-Taupin equations used in their numerical solution, only the algorithm for solving the Takagi-Taupin equations where the displacement field function enters in exponential form is acceptable in terms of the required accuracy-duration of the calculations.

Forecasting the cutting force in end milling

The object of this study is the process of end milling, taking into account the discontinuity of the process, simultaneous cutting with several flutes arranged in a spiral, tool runout, and feedback in the elastic machining system, in particular, for the depth of cutting. The subject of the study is the cutting force and identification of its empirical model. During identification, the cutting force coefficient is automatically determined when matching the theoretical and experimental oscillograms of the cutting force component. The reported results related to forecasting the cutting force at end milling are based on a mechanistic approach and involve the process modeling method for forecasting. The simulation uses an algorithm for representing the interaction of the cutter flutes workpiece engagement, based on the scan of the cutter according to the rotation angle coordinate. The algorithm makes it possible to identify empirical coefficients and exponents of the cutting force model based on experimental oscillograms of cutting force components. The built model is implemented in an application program and owing to the representation of the machining system in the form of a closed structural diagram, it allows predicting the elastic displacement, which will determine the actual cutting depth. The developed program under an interactive mode using digital files of experimental cutting force components makes it possible to perform model identification and predict cutting force components with an error of 4.6 %. The adequacy of the algorithms was confirmed by measuring the profile of the machined surface in the places where the cutting mode changed with the feed stopped. The developed simulation algorithm makes it possible to take into account the simultaneous cutting by several flutes arranged in a spiral, the runout of the tool, and the feedback in the elastic machining system, in particular, the depth of cutting

Seismic Capacity of Reinforced Concrete Eccentric Braced Frame (EBF) With Vertical Link Using 20% GGBFS

EBF-V bracing is highly attractive due to its good seismic performance in high seismic zones. Vertical link beams as a component are capable of high elastic displacement and ductility to absorb lateral forces through shear-bending collapse mechanisms. However, the lateral load capacity of the bracing has to be sacrificed as it tends to decrease. The present study focuses on the capacity and lateral behavior of reinforced concrete eccentrically braced frame (EBF) with vertical link beam and tighter reinforcement spacing in the link beam in combination with GGBFS. GGBFS at 20% can improve the mechanical properties by reducing the pore number of the concrete due to the smaller particle size of OPC.This study uses CBF-V as a control to investigate the seismic behavior of tightly spaced transverse reinforcement (75 mm) in EBFs’s vertical link beam with eccentricities of 15 cm and 25 cm. In addition, the role of GGBFS was also observed through the displacement and ductility of the frame. As a result, the CBF has the highest plasticity. However, the tight reinforcement spacing of the vertical link beam in the EBF-V-15 results in the highest restraint, resulting in excellent stiffness and ductility through earthquake absorption with a shear collapse mechanism. In addition, GGBFS also plays a role in improving the collapse mechanism, which is characterized by large elastic displacement and high ductility.

Constant-Head Step-Injection Tests Using a Conventional Straddle-Sliding-Packer System for Investigating the Shear Capabilities of Minor Faults

Low-permeability rock is suitable as the host rock of an underground repository for radioactive waste disposal; however, minor faults might develop there. Investigating the shear capability (= shear compliance) of those faults is crucial because they could be elastically sheared by the thermal effect of the waste to damage the waste’s engineered barriers. This study performed constant-head step-injection tests along with a recently developed packer-pressure-based extensometer method for assessing the applicability of this method to investigate the shear capability of minor faults. Herein, two neighboring minor faults (A and B) in siliceous mudstone were evaluated. The results showed that fault A, with centimeter-thick fault breccia, exhibited high shear capability, whereas fault B, with millimeters or less-thick fault breccia, displayed low shear capability despite containing an incohesive fault rock. An elastic shear displacement occurred for fault A during injection and reached 15–66 mm when the test-section pressure increased from 4.1 to 4.3 MPa. Here, the shear capability was 101 mm/MPa or more. Conversely, fault B had cohesion, and no shear displacement was detected even when the test-section pressure increased from 4.0 to 6.0 MPa. In this case, the shear capability was 10−1 mm/MPa or less. The estimated shear capabilities were consistent with the results from previous shear experiments, and therefore, the applied method helps investigate the shear capabilities of minor faults.

The internal ballistics of a spring gun

We consider the features of pellet motion under the elastic force acting from a decompressing spring of a finite mass. The muzzle speed of the pellet decreases as the ratio between spring and pellet mass increases. In the general case, the pellet loses contact with the spring as it is stretched. This effect occurs due to the fact that the peak of elastic displacement wave, propagating from the fixed end, reaches the opposite end of the spring. With a large relative mass of the pellet, it accelerates along a quarter of the sinusoid. At the limit of a very small pellet mass, it moves nearly all the time along with the end of the spring at an almost constant speed, approximately equal to the speed of sound propagation in the spring. In this case, after the initial compression, the pellet passes the equilibrium position, and comes off after moving a similar distance beyond the equilibrium.

Large displacement model for the nonlinear behaviour of the face plate component

This paper deals with the face plate component in steel joints and addresses the full characterization of the nonlinear behaviour of the face plate component. An equivalent beam strip model is proposed that tackles the connection of a beam to the column web of open I-sections in a minor axis joint or the face of tubular columns, covering endplate or fin plate joint typologies. Closed-form analytical solutions are obtained for the elastic large displacement and the elastic-plastic large displacement behaviour of the equivalent beam strip. Criteria for the establishment of the design resistance using the continuous strength method are also proposed. It was concluded that the model is easy to apply, was validated against a large parametric study using finite element beam models, leads to accurate solutions and demonstrates the need to consider membrane effects in design.

Hysteretic models with damage and flexibility increase

The need to accurately describe nonlinear degrading phenomena in both modern and classical complex materials that exhibit hysteretic behavior is a relevant task for the analysis of their response. In the present study an enrichment to an existing formulation to describe strength and stiffness degradation is proposed. The description of damage, that reduces the hysteretic force, is then accompanied by the introduction of flexibility increase, which increments the elastic displacement experienced by the system. Both effects influence the energy dissipated by the system. The condition of thermodynamic admissibility in presence of damage and flexibility increase is derived, entailing constraints on system parameters. Additional constraints arise from consistency conditions on the transformation of the pure hysteretic system into the system with damage and flexibility increase. A numerical solution involving the forward Euler method is presented to evaluate the response quantities. The formulation is eventually applied to the elastic–plastic and Bouc Wen hysteresis models, and the influence of the degrading parameters is presented. The presented Bouc-Wen model with damage and flexibility increase is applied to study the cyclic response of a masonry panel experimentally tested to validate the numerical model and prove its capability of describing the structural response.

Thermoviscoelastic response of skin tissue via fractional Pennes bioheat and fractional viscoelasticity

In this paper, the thermoviscoelastic response of skin tissue, as a typical class of viscoelastic biological tissue, subject to thermal shock is studied based on the fractional Kelvin-Voigt model and fractional Pennes bioheat conduction. A time-fractional biothermoviscoelastic governing equation is derived and initial-boundary value conditions are given for monolayer skin tissue of finite thickness. The temperature change and thermal stress of viscoelastic skin tissue are obtained by the Laplace transform and its inversion using matlab software. The influences of viscosity coefficient, relaxation times, fractional-order viscosity/heat parameter, and blood perfusion rate of skin tissue on the temperature distribution and the elastic displacement are analyzed. The numerical results show that fractional-order viscosity does not affect temperature, whereas fractional-order heat flow does. Moreover, fractional-order heat flow affects the sensitivity of blood perfusion rate to the thermodynamic response.

Mechanical analysis of frost heaving of weakly cemented soft rock tunnels in cold regions

To reveal the mechanical response of non-uniform frost heave of surrounding rock in soft rock tunnel in cold region, the stress solution of frozen surrounding rock considering the temperature field was deduced by applying elastic mechanics' displacement potential theory and the superposition principle. Then the plastic zone evolution of frozen surrounding rock was clarified by using the limit equilibrium approach. Furthermore, the analytical solution is verified with the existing solutions, and proved to be reasonable. The calculation results showed that as the temperature drops, the growth rate of the frozen zone radius gradually slows down while the stress increment increases. Frost heaving effect lead to a decrease in the critical state value of the lateral pressure coefficient (λ) for tension–compression. Circumferential stresses show a significant stress drop at the frozen boundary, and radial stresses show extreme values. Frost heaving enlarges the circumferential range of the plastic zone. Under low initial vertical stress conditions (p), when λ or 1/λ decreases from 1 to 0, the plastic zone gradually increases, while its range is always in the frozen zone. However, with an increase in “p” and a decrease in temperature to a certain extent, both inner and outer plastic zones emerged.

Design and Analysis Method of Piezoelectric Liquid Driving Device with Elastic External Displacement.

In piezoelectric drive, resonant drive is an important driving mode in which the external elastic force and electric drive signal are the key factors. In this paper, the effects of the coupling of external elastic force and liquid parameters with the structure on the vibrator resonance frequency and liquid drive are analyzed by numerical simulation. The fluid-structure coupling model for numerical analysis of the elastic force was established, the principle of microdroplet generation and the coupling method of the elastic force were studied, and the changes in the resonant frequency and mode induced by the changes in the liquid parameters in different cavities were analyzed. Through the coupled simulation and calculation of the pressure and deformation of the cavity, the laser vibration measurement test was carried out to test the effect of the vibration mode analysis. The driving model of the fluid jet driven by the elastic force on the piezoelectric drive was further established. The changing shape of the fluid jet under different elastic forces was analyzed, and the influence law of the external elastic force on the change in the droplet separation was determined. It provides reference support for further external microcontrol of droplet motion.