Three-dimensional Elastic Analysis Research Articles

On a 3D material modelling of smart nanocomposite structures

Smart composites (SCs) are utilized in electro-mechanical systems such as actuators and energy harvesters. Typically, thin-walled components such as beams, plates, and shells are employed as structural elements to achieve the mechanical behavior desired in these composites. SCs exhibit various advanced properties, ranging from lower order phenomena like piezoelectricity and piezomagneticity, to higher order effects including flexoelectricity and flexomagneticity. The recently discovered flexomagneticity in smart composites has been investigated under limited conditions. A review of the existing literature indicates a lack of evaluation in three-dimensional (3D) elasticity analysis of SCs when the flexomagnetic effect (FM) exists. To address this issue, the governing equations will incorporate the term ∂/∂z, where z represents the thickness coordinate. The variational technique will guide us in further developing these governing equations. By using hypotheses and theories such as a 3D beam model, von Kármán's strain nonlinearity, Hamilton's principle, and well-established direct and converse FM models, we will derive the constitutive equations for a thick composite beam. Conducting a 3D analysis implies that the strain and strain gradient tensors must be expressed in 3D forms. The inclusion of the term ∂/∂z necessitates the construction of a different model. It should be noted that current commercial finite element codes are not equipped to accurately and adequately handle micro- and nano-sized solids, thus making it impractical to model a flexomagnetic composite structure using these programs. Therefore, we will transform the derived characteristic linear three-dimensional bending equations into a 3D semi-analytical Polynomial domain to obtain numerical results. This study demonstrates the importance of conducting 3D mechanical analyses to explore the coupling effects of multiple physical phenomena in smart structures.

Tourists’ travel mode and length of stay: Application of a fully nested Archimedean copula structure

Tourism decisions are interdependent of one another. This study aims to explore the interrelations among three pertinent tourism choices, i.e., travel season, transport mode and length of stay, from a data-driven perspective. To achieve a joint model of three travel behavioural decisions, this paper adopts a Frank-type fully nested Archimedean copula function, which is capable of efficiently incorporating a logistic regression model, a multinomial logit model and a lognormal accelerated failure time model. Then, we empirically evaluate the proposed model framework using single-destination Sydney-based trip-level data collected in 2017–2018. Gumbel, Clayton and Frank copula results are compared. To illustrate its application, the modelling results are used to build a simulated COVID-19 pandemic scenario according to the social distancing restrictions within New South Wales, Australia, and a three-dimensional elasticity analysis for trip destinations is performed. The findings suggest the model provides nuanced insights into simulating tourist behaviours and transport policy appraisal aimed at tourism recovery or/and development.

Three-Dimensional Thermo-Mechanical Elastic Analysis of Functionally Graded Five Layers Composite Sandwich Plate on Winkler Foundations

In this work, the first shear deformation theory (FSDT) is used for the thermo-mechanical analysis of a simply supported five-layer functionally Graded (FG) sandwich plate resting on a Winkler elastic foundation. The sandwich plate consists of five layers (two functionally graded face sheets (AL−AL2O3), with aluminum (Al) as the metal and Alumina (AL2O3) as ceramic phases. Two vinyl ester adhesive layers bond the face sheets to an Elastollan core. The governing equations are obtained using the principle of virtual displacements. A uniform distributed load q with constant magnitude is applied on the top face sheet while all layers experience a steady temperature equal to T. We adapted layerwise theory (LT) to solve each layer’s stress distribution. Navier solution is employed to produce the semi-analytical solution results, which are compared with those of three-dimensional finite element analysis obtained by ABAQUS software. A parametric study is presented to observe the effect of the material gradation, variation in plate dimensions, variation in the thermo-mechanical load, and elastic foundation on the deflections and stresses in the functionally graded sandwich plate. For a composite sandwich plate with mechanical load, in the absence of thermal load, results of the first-order shear layer theory obtained by using the Navire method are relatively good in comparison to the normal stresses obtained for investigated points, which are obtained by finite element.

Three-dimensional elastic analysis of a bi-material system with a single domain boundary element method

The three dimensional fundamental solution of bi-materials is introduced to the boundary element method (BEM) for elastic analysis of a bi-material system instead of solving a multi-domain problem. Using the explicit form of the Green’s function for bi-materials, the boundary integral equations (BIE) are set up for a finite bi-layered material system with a plane interface. The Green’s function for a bi-material system combines the Kelvin’s solution and disturbed fields by image source. Because it exactly satisfies the jointed continuity conditions at the interface (x3=0), no internal mesh is required along the interface and a single domain BEM can be established. The potential numerical errors of the multi-domain BEM using the Kelvin’s solution due to the mesh quality at the interface can be avoided. This single domain BEM for bi-material saves the effort of domain discretization, predicts the singularity on the interface analytically, and enables an efficient, straightforward analysis similar to the homogeneous solids. It is particularly suitable to simulate thin film/substrate systems, overlay/base structures, and other similar layered materials. The numerical simulations verify the effectiveness and convergence of the method, and the case studies of wind turbine blades and solar panels demonstrate the industrial applications of this method.

Influence of Perforated Soils on Installation of New Piles

In recent years, there has been an increasing demand to replace ancient structures. The removal of such structures also involves the removal of the existing piles that supported the structures, and the backfilling of the pulling-out holes that formed during the removal. However, there are no standard guidelines for the backfilling of pulling-out holes. At present, therefore, each owner or contractor must determine the material and the construction method to use for backfilling. This results in a difference between the mechanical properties of the original soil and those of the soil that has been backfilled, namely, the soil on which a newly built structure will be constructed. In this study, it was assumed that a new pile would be installed on a perforated soil (that is, the soil left after removing the existing piles) where the mechanical properties differ between the original soil and the backfilled soil. The behavior of the new pile, when installed on the boundary of a soil between two types of mechanical properties, was evaluated by a three-dimensional linear elastic analysis. When the new pile was installed at the boundary between the two types of soil with different mechanical properties, most of the new pile was inclined to the soil side where the N value was relatively small. However, the inclination of the new pile was able to be suppressed by increasing the distance from the boundary between the two types of soil.

Finite Element Analysis of Wave Barriers Used to Reduce Train Induced Vibrations

The finite element method is used to simulate the soil vibration behavior due to the Basrah-Baghdad passenger train and its effect on a targeted building in the Al-Ma'qal quarter, Basrah governorate. Three-dimensional dynamic elastic analyses are performed to calculate the particle velocities for a train speed of 120 km/hr. The effectiveness of screening using active (10 m long) open trench barriers with variable depth (2 m - 5 m) and width (0.4 m - 0.8 m), is being studied. For a given trench width (0.4 m), the results of the parametric study revealed a considerable effect of trench depth where the screening capability near the trench is increased by (10.4 %, 26.1 %, 36.3 %) due to a (50 %, 100 %, 150 %) increase in depth. The results are less sensitive to the variation in trench width. The screening capability of a double open (0.4 m × 10 m × 2 m) trench system was also investigated, where a mitigation improvement of (36.4 %) was achieved. The vibration mitigation using single and double trench systems, filled with (40 %) rubber content mixture, was also analyzed. It is concluded that using the additional passive trench increases the mitigation of the single system by around 19.1 %. An important finding is that the (40 % rubber + 60 % native cohesive soil) mixture proved to be a good filling material, since the infilled-trench systems produced comparable screening ratios to the open systems, where (97.7 %) and (85.4 %) were accomplished for the single and double systems, respectively.

"An Elastic Finite Element Analysis of the C2-C7 Human Cervical Spine Segment"

A three-dimensional linear elastic FE analysis of six adjacent cervical vertebrae (C2- C7) has been developed. The model is composed of vertebrae and intervertebral discs. The objective of this research is to address the new advances in the generation of finite element meshes of the human cervical spine...

Three-dimensional exact elastic analysis of nanoplates

Three-dimensional exact elastic analysis of nanoplates

Modified couple stress theory for three-dimensional elasticity in curvilinear coordinate system: application to micro torus panels

This research considers size effects in the linear three-dimensional elasticity analysis of micro-tori. The fundamental relations (displacement form) are derived for isotropic toroidal shells in the framework of the modified couple stress theory in the curvilinear coordinate system to predict the mechanical responses. A numerical solution for the displacement field is obtained using the GDQ method. The numerical results are in a close agreement with those found by the finite element and the Galerkin method. Parametric studies are conducted to explore the effect of size-dependency, micro-tori geometry, meridional and circumferential angle, toroidal shell thickness, and different boundary conditions on the distribution of the displacement fields. Numerical results for displacement also show that natural frequencies of micro-toroidal shells, predicted by modified couple stress theory, are less than those predicted by the classical theory, due to the significant effect of length scale parameter (related to material microstructures) on the mechanical responses. The use of general curvilinear coordinates in toroidal structures enables us to also study the mechanical behavior of irregular geometries, cap-shaped panel, saddle-shaped panel, and sectorial-shaped panel.

Prying action in an elastic T-stub tensile connection

We investigate a bolted T-stub joint in tensile loading as an elastic receding contact problem. In this configuration two flat flanges are fastened together by bolt tension and are subjected to central tension loading, possibly cyclic. Due to the bending flexibility of the flanges, large “prying” contact forces arise which can cause the bolt forces to exceed the applied load. Hence such joints may be prone to failure especially under repeated loading. This elastic analysis is suitable to determine the onset of plastic yield and to investigate fatigue failure.In many design procedures the analysis of a T-stub joint is based on the assumption of lift-off of the entire flange except its outer edges. We treat the T-stub joint as a compliant receding contact problem where the flexural deformation of the components induces variable-location prying forces. We show that the traditional approach can significantly underestimate the prying forces in cases where the prying forces act nearer to the bolt. Our analysis also demonstrates that, in cases in which the predicted lift-off distance is greater than the distance to the flange edge, the use of a longer flange would be protective of the bolt. We present results for the elastic T-stub bolt force based on two beam theories, as well as a sampling of results using three-dimensional finite element elasticity analysis. We also propose a formula for flange thickness that suppresses prying, and interpret our results via the Goodman fatigue criterion to define the required steel-bolt ultimate strength under cyclic loading.

Design equation to evaluate bursting forces at the end zone of post-tensioned members

Design equations to evaluate the bursting force in a post-tensioned anchorage zone have been introduced in many design codes, and one equation in AASHTO LRFD is widely used. However, this equation may not determine the bursting force exactly because it was designed on the basis of two-dimensional numerical analyses without considering various design parameters such as the duct hole and shape of the bearing plate. To improve the design equation, modification of the AASHTO LRFD design equation was considered. The behavior of the anchorage zone was investigated using three-dimensional linear elastic finite element analysis with design parameters such as bearing plate size and diameter of sheath hole. Upon the suggestion of a modified design equation for evaluating the bursting force in an anchorage block with a rectangular anchorage plate (Kim and Kwak 2018), additional influences of design parameters that could affect the evaluation of bursting force were investigated. An improved equation was introduced for determining the bursting force in an anchorage block with a circular anchorage plate, using the same procedure introduced in the design equation for an anchorage block with a rectangular anchorage plate. The validity of the introduced design equation was confirmed by comparison with AASHTO LRFD.

Development of a fiber-reinforced material for fiber posts: Evaluation of stress distribution, fracture load, and failure mode of restored roots

Statement of problemThe biomechanical behavior of post-restored roots with an experimental fiber-reinforced composite resin is unknown. PurposeThe purpose of this in vitro study was to investigate the biomechanical behavior of an experimental composite resin (3-mm short glass fiber incorporated in methacrylate matrix with filler particles) used to produce the custom post itself or to reline fiber posts. Material and methodsFour testing groups (n=10) were created according to the root restoration method: FG, commercially available fiber post; FG+RC, fiber post relined with conventional composite resin; FG+EXP, fiber post relined with the experimental composite resin; and EXP, a custom post made of experimental composite resin. A three-dimensional finite element linear elastic analysis was performed by using geometric representations of groups, and the results were analyzed by von Mises (σvM) and maximum principal stress criteria. In sequence, 40 bovine incisors were assigned to these groups and subjected to a fracture load test (Instron 5965; 0.5 mm/min), and the failure mode was determined. ResultsThe EXP group showed more homogeneous stress distribution for σvM. ANOVA and the Tukey honestly significant difference (HSD) tests showed significant differences (P<.001) in fracture load (mean ±standard deviation; different superscript letters indicate statistical difference): FG+EXP (669.5 ±107.7)A; FG (620.7 ±59.2)A; EXP (506.5 ±27.0)B; FG+RC (452.7 ±81.6)B. No differences were found for failure mode (P=.595). ConclusionsThe experimental composite resin significantly increases fracture load when used to reline commercially available fiber posts and, irrespective of its use, presented lower stress concentration.

Three-dimensional elasticity analysis of sandwich panels with functionally graded transversely isotropic core

In this paper, three-dimensional elastic deformation of rectangular sandwich panels with functionally graded transversely isotropic core subjected to transverse loading is investigated. An exponential variation of Young’s and shear moduli through the thickness is assumed. The approach uses displacement potential functions for transversely isotropic graded media and a three-dimensional elasticity solution for a transversely isotropic graded plate developed by the authors. The effects of transverse shear modulus, loading localisation, panel thickness and anisotropy on the stresses and displacements in the panel are examined and discussed.

An extended state space method for three-dimensional elasticity analysis of arbitrary graded sandwich plates

A novel procedure, within the framework of the state space method in linear elasticity, is proposed for three-dimensional analysis of simply supported, multi-layered plates including any number of arbitrary graded layers at arbitrary locations along the transverse coordinate. First, the conventional state space method used for single layer exponentially graded plates is extended to multi-layered plates including any number of exponentially graded layers. This is achieved by incorporating additional matrices for implementing continuity of the state variables at interfaces involving at least one exponentially graded layer. Further, a piece-wise exponential model is used to extend the procedure to plates that include any number of layers whose material properties vary as arbitrary smooth functions along the transverse coordinate. Comparisons with existing elasticity and approximate solutions show that the method is capable of providing numerical results with better accuracy for all the cases studied. New results are obtained for three-dimensional deformation analysis of sandwich plates with graded face sheets and graded soft core, including a detailed parametric study.

Bending analysis of anisotropic functionally graded plates based on three-dimensional elasticity

Although theories of plates are accurate enough to use for thin plates, the three-dimensional elasticity analysis is needed to study the thick plates, which increases the computational efforts. The...

A novel rapid method of purely elastic solution correction to estimate multiaxial elastic-plastic behaviour

Abstract In structural analysis, it is of paramount importance to assess the level of plasticity a structure may experience under monotonic or cyclic loading as this may have a significant impact, particularly in fatigue analysis for singular areas. For efficient design analyses, it is often searched for a compromise in accuracy that consists in correcting a purely elastic analysis, generally simpler and faster to obtain compared to a full non-linear Finite Element (FE) analysis involving elastic-plastic behaviour, to estimate the actual elastic-plastic solution. There exists a great number of correction techniques in the literature among which the most famous and commonly used are Neuber and ESED energy-based methods. Nonetheless, both of them are known to provide respectively upper and lower bounds of the exact solution in most cases, with a relative deviation depending on the level of multiaxiality and on the amount of stress redistribution due to yielding. The new methodology presented in this paper is based on the well-known multiaxial Radial Return Method (RRM) revisited using effective parameters approach. By essence, it is fast and can be applied either to analytical elastic problems or to more complex three-dimensional elastic FE analyses. The accuracy of the proposed method is assessed by direct comparison with results from Neuber and ESED methods on various examples. It is also shown for each of them that this new method is very good agreement with the exact elastic-plastic solution. Highlights A new technique of purely elastic solution correction is presented and evaluated. The proposed method relies on the modification of Return Radial Method (RRM) considering effective parameters in lieu of initial elastic tensor. The obtained equation preserves the simplicity and efficiency of other well-known energy-based methods such as Neuber and ESED. It is shown on several examples that the proposed technique is in very good agreement with the exact or FE elastic-plastic solution, with very low relative deviation.

Three-Dimensional Elastic Analysis of a Structure with Holes Using Accelerated Coupling-Matrix-Free Iterative s-Version FEM

Some improvements of the coupling-matrix-free iterative s-version finite element method (FEM) to shorten its computational time are proposed. Then, the proposed method is applied to three-dimensional stress concentration problems. For sufficiently small computational time for practical use, two key techniques are introduced. First, the iteration is accelerated drastically by using the proposed convergence acceleration techniques. Secondly, stress transfers between global and local meshes are accelerated considerably by a bucket search algorithm. The proposed method was more than one hundred times faster than the straightforward algorithm of the coupling-matrix-free iterative s-version FEM.

Three-Dimensional Elastic Analysis of Rock Excavations by Using the g2 Constant Displacement Discontinuity Method

A fast computational code is presented that is dedicated for the elastic analysis of three-dimensional excavations and cracks in rocks. The problem is solved on the boundaries that are discretized with a new triangular leaf constant displacement discontinuity element with one collocation point. The creation of the new triangular element was inspired from Mindlin's special version of grade-2 or strain-gradient elasticity theory (second gradient of displacement, g2). This element is characterized by a much better measure of the average stress at the center of gravity of the triangular element compared to that of the classical elasticity element close to regions with stress or strain gradients (e.g. notches, cracks etc). In a verification stage, the accuracy of the computational algorithm for the pressurized penny-shaped and mixed-mode elliptical crack problems that have analytical solutions is demonstrated. More specifically, it is shown that the average error of the crack tip Stress Intensity Factor predicted by the gradient modified method for nine discretizations of varying density is around 3.5% with a máximum error of 5%, while the constant displacement discontinuity element displays errors varying around 14%. Moreover, the new method preserves the simplicity and hence the high speed of the constant displacement discontinuity with only one collocation point per element, but it is far more efficient compared to it, especially close to the crack tips and corners of excavations where the displacement and stress gradients are highest.

被覆層－基質物体のインデンテーション法における三次元弾性理論解析

被覆層－基質物体のインデンテーション法における三次元弾性理論解析

On Saint-Venant's Problem for Helicoidal Beams

This paper proposes a novel solution strategy for Saint-Venant's problem based on Hamilton's formalism. Saint-Venant's problem focuses on helicoidal beams and its solution hinges upon the determination of the subspace of the system's Hamiltonian matrix associated with its null and pure imaginary eigenvalues. A projection approach is proposed that reduces the system Hamiltonian matrix to a matrix of size 12 × 12, whose eigenvalues are identical to the null and purely imaginary eigenvalues of the original system, with the same Jordan structure. A fundamental theoretical result is established: Saint-Venant's solutions exist because rigid-body motions create no strains. Indeed, the solvability conditions for the governing equations of the problem are satisfied because a matrix identity holds, which expresses the fact that rigid-body motions create no strains. Because it avoids the identification of the Jordan structure of the original system, the implementation of the proposed projection for large, realistic problems is straightforward. Closed-form solutions of the reduced problem are found and three-dimensional stress and strain fields can be recovered from the closed-form solution. Numerical examples are presented to demonstrate the capabilities of the analysis. Predictions are compared to exact solutions of three-dimensional elasticity and three-dimensional FEM analysis.