Line strain representation and shear strain representation of 3D strain states

The strain state in 3D space is usually expressed by the conventional method of combining three linear and shear strains. Due to the obvious differences between the first two strains, it is necessary to uncover their properties when describing deformation, studying yield and failure, and developing test apparatus or equipment. The difficulties encountered in the above work would be greatly simplified if strain states could be expressed in a single strain form, namely including only linear or shear strains. As a start, this paper explores the meaning and nature of strain states. Then, based on the hypothesis of small deformations, two strain state expressions, the linear strain expression method (LSEM) and shear strain expression method (SSEM), were established for incompressible materials with only linear strain and shear strain as parameters respectively. Furthermore, conditions, implementation steps and specific forms for the application of SSEM in 1D, 2D and 3D strain states are obtained. As an example, two representations based on tetragonal pyramid and rotating tetrahedron are especially given. Therefore, conventional strain representation methods can be expressed as a combination of line strains in a certain direction or a combination of characteristic shear strains. The results of this paper provide a new way for understanding deformation characteristics, revealing yielding process, establishing constitutive models, and developing testing apparatus or equipment.

Fuzzy logic aided PPF controller design to active vibration control of a flexible beam

This paper presents a fuzzy-logic-based observer and a positive position feedback controller to reduce a standard beam's free vibrations using a piezoelectric actuator. It is aimed that fuzzy-logic-based observer is used as feed-through and improves the overall performance of the PPF controller. For this aim, the cantilever beam and a piezoelectric patch are initially numerically modeled using the finite element method considering the close loop control algorithm. The displacement and strain responses results are compared with the experimental model. Then, two controllers are applied to the designed system: positive position feedback (PPF) and fuzzy-logic-based positive position feedback (FLBPPF). The uncontrolled and controlled system responses are investigated and compared in terms of the linear strain and tip displacement results. Using the FLBPPF controller, the settling times of controlled systems are decreased by about 20.7% and 41.6% regarding the linear strain and tip displacement response compared to the PPF controller.

Strain maps characterize the symmetry of convergence and extension patterns during zebrafish gastrulation

During gastrulation of the zebrafish embryo, the cap of blastoderm cells organizes into the axial body plan of the embryo with left–right symmetry and head–tail, dorsal–ventral polarities. Our labs have been interested in the mechanics of early development and have investigated whether these large-scale cell movements can be described as tissue-level mechanical strain by a tectonics-based approach. The first step is to image the positions of all nuclei from mid-epiboly to early segmentation by digital sheet light microscopy, organize the surface of the embryo into multi-cell spherical domains, construct velocity fields from the movements of these domains and extract strain rate maps from the change in density of the domains. During gastrulation, tensile/expansive and compressive strains in the axial and equatorial directions are detected as anterior and posterior expansion along the anterior–posterior axis and medial–lateral compression across the dorsal–ventral axis and corresponds to the well characterized morphological movements of convergence and extension. Following gastrulation strain is represented by localized medial expansion at the onset of segmentation and anterior expansion at the onset of neurulation. In addition to linear strain, symmetric patterns of rotation/curl are first detected in the animal hemispheres at mid-epiboly and then the vegetal hemispheres by the end of gastrulation. In embryos treated with C59, a Wnt inhibitor that inhibits head and tail extension, the axial extension and vegetal curl are absent. By analysing the temporal sequence of large-scale movements, deformations across the embryo can be attributed to a combination of epiboly and dorsal convergence-extension.

A novel specimen shape for measurement of linear strain fields by means of digital image correlation

Strains on the surface of engineering structures or biological tissues are non-homogeneous. These strain fields can be captured by means of Digital Image Correlation (DIC). However, DIC strain field measurements are prone to noise and filtering of these fields influences measured strain gradients. This study aims to design a novel tensile test specimen showing two linear gradients, to measure full-field linear strain measurements on the surface of test specimens, and to investigate the accuracy of DIC strain measurements globally (full-field) and locally (strain gauges’ positions), with and without filtering of the DIC strain fields. Three materials were employed for this study: aluminium, polymer, and bovine bone. Normalized strain gradients were introduced that are load independent and evaluated at two local positions showing 3.6 and 6.9% strain change per mm. Such levels are typically found in human bones. At these two positions, two strain gauges were applied to check the experimental strain magnitudes. A third strain gauge was applied to measure the strain in a neutral position showing no gradient. The accuracy of the DIC field measurement was evaluated at two deformation stages (at $$\approx $$ ≈ 500 and 1750 μstrain) using the root mean square error (RMSE). The RMSE over the two linear strain fields was less than 500 μstrain for both deformation stages and all materials. Gaussian low-pass filter (LPF) reduced the DIC noise between 25% and 64% on average. As well, filtering improved the accuracy of the local normalized strain gradients measurements with relative difference less than 20% and 12% for the high- and low-gradient, respectively. In summary, a novel specimen shape and methodological approach are presented which are useful for evaluating and improving the accuracy of the DIC measurement where non-homogeneous strain fields are expected such as on bone tissue due to their hierarchical structure.

Opto-mechanical modeling and experimental implementation of an FBG-based piezoelectric bimorph actuator for high voltage sensing applications

This paper proposes a highly simplified optical voltage sensor by using a piezoelectric bimorph and a Fiber Bragg Grating (FBG) that can be used for high voltage applications with a relatively good accuracy and stability. In this work the theoretical framework for the whole opto-mechanical operation of the optical sensor is detailed and compared to experimental results. In the analysis, a correction term to the electric field is derived to account for the linear strain distribution across the piezoelectric layer improving the designing equations and giving more criteria for future developments. Finally, some experimental results from a laboratory scale optical-based high voltage sensing setup are discussed, and shown to be in excellent agreement with theoretical expected behavior for different voltage magnitudes.

Analysis of Crustal Movement and Deformation in Mainland China Based on CMONOC Baseline Time Series

In this paper, we propose a method for the analysis of tectonic movement and crustal deformation by using GNSS baseline length change rates or baseline linear strain rates. The method is applied to daily coordinate solutions of continuous GNSS stations of the Crustal Movement Observation Network of China (CMONOC). The results show that: (a) The baseline linear strain rates are uneven in space, which is prominent in the Tianshan, Sichuan-Yunnan, Qinghai-Tibet Plateau, and Yanjing areas, with a maximum value of 1 × 10−7 a−1, and about two orders smaller in the South China block, the Northeast block, and the inner area of the Tarim basin, where the average baseline linear strain rates are 1.471 × 10−9 a−1, 2.242 × 10−9 a−1, and 3.056 × 10−9 a−1, respectively; (b) Active crustal deformation and strong earthquakes in the Xinjiang area are mainly located in the north and south sides of the Tianshan block; the compression deformations both inside the Tarim block and in the southern Tianshan fault zone are all increasing from east to west, and the Tarim block is not a completely “rigid block”, with the shrinkage rate in the west part at about 1~2 mm/a; (c) The principal directions of crustal deformation in the Xinjiang, Tibet, and Sichuan-Yunnan regions are generally in the north—south compression and east—west extension, indicating that the collision and wedging between the Indian and Eurasian plates are still the main source of tectonic movements in mainland China.

Neural Network-Based Prediction Model to Investigate the Influence of Temperature and Moisture on Vibration Characteristics of Skew Laminated Composite Sandwich Plates

The present study deals with the development of a prediction model to investigate the impact of temperature and moisture on the vibration response of a skew laminated composite sandwich (LCS) plate using the artificial neural network (ANN) technique. Firstly, a finite element model is generated to incorporate the hygro-elastic and thermo-elastic characteristics of the LCS plate using first-order shear deformation theory (FSDT). Graphite-epoxy composite laminates are used as the face sheets, and DYAD606 viscoelastic material is used as the core material. Non-linear strain-displacement relations are used to generate the initial stiffness matrix in order to represent the stiffness generated from the uniformly varying temperature and moisture concentrations. The mechanical stiffness matrix is derived using linear strain-displacement associations. Then the results obtained from the numerical model are used to train the ANN. About 11,520 data points were collected from the numerical analysis and were used to train the network using the Levenberg–Marquardt algorithm. The developed ANN model is used to study the influence of various process parameters on the frequency response of the system, and the outcomes are compared with the results obtained from the numerical model. Several numerical examples are presented and conferred to comprehend the influence of temperature and moisture on the LCS plates.

Variation in Poison’s Ratio with Change in Grade of Concrete and Type of Steel Reinforcement

The structure that are widely used around the gold now days are mainly composite structure. These types of models or structures are used to make long span lower story heights and also to give extra stiffness. The past result shows that most of the collapses of buildings occur when the structure is struck with earthquake or seismic load. The poison’s ratio is one of the most integral part which gives stability for the structure. In this research it is about the change is the poison’s ratio that occurs with the change in percentage of steel and the grade of concrete in a reinforced concrete section. The variation in poisons ratio shows the variation in the stability of the structure. The study of the poisons ratio will help in a better practical design of the structure to prevent or the resist the structure from collapse during earthquake. In this paper we will see the experimental variation of the poisons ratio of column and we will analysis the behavior using software. Poison’s ratio usually deals with the lateral strain and linear strain. This poisons ratio was found out by Simeon poison. It is one of the most important aspects in the design of any kind of structure.

The Vibration of a Beam under a Traversing Load

The objective of this study is to investigate the response of an Euler-Bernoulli beam under a force or mass traversing with constant velocity. Simply-supported and clamped-clamped boundary conditions are considered. The linear strain-displacement scenario is applied to both boundary conditions, while the von Kármán nonlinear scenario is applied only to the former boundary condition. The governing equation of motion is derived via the extended Hamilton's principle. Simulations are performed with the fourth-order Runge-Kutta method via Matlab software. The equation of motion is first validated and then used to investigate the effects of the beam second moment of area, the magnitude of the traversing velocity, and centrifugal and gyroscopic forces.

The Vibration of a Beam under a Traversing Load

The objective of this study is to investigate the response of an Euler-Bernoulli beam under a force or mass traversing with constant velocity. Simply-supported and clamped-clamped boundary conditions are considered. The linear strain-displacement scenario is applied to both boundary conditions, while the von Kármán nonlinear scenario is applied only to the former boundary condition. The governing equation of motion is derived via the extended Hamilton's principle. Simulations are performed with the fourth-order Runge-Kutta method via Matlab software. The equation of motion is first validated and then used to investigate the effects of the beam second moment of area, the magnitude of the traversing velocity, and centrifugal and gyroscopic forces.