Load Boundary Research Articles

A unified formulation for axial compression of steel tube-confined concrete and concrete-filled steel tube stub columns

Steel-confined concrete (STCC) columns and concrete-filled steel tube (CFST) columns have different load boundary conditions. In STCC columns, the steel tube transmits minimal axial load. Existing design practices employ different formulas to predict the axial load-bearing capacity of STCCs and CFSTs based on these varying load boundary conditions. However, there has always been a practical and challenging demand for researchers and engineers to develop a unified design formula that accommodates composite columns with different sections and load boundary conditions. This demand aligns with the contemporary design concept of continuous structural design optimization. This paper proposes an analytical solution for the elastic deformation of circular STCCs under axial compression, considering the specific load boundary conditions in circular STCC columns. This solution is then extended to encompass polygonal sections, resulting in a unified formula for determining the strength of STCC columns. Additionally, the influence of load boundary conditions on the confined effect of the core concrete is quantified by reformulating and simplifying the proposed formula. These adjustments are informed by the formulation for the axial load capacity of CFST columns proposed by Yu Min et al. Finally, a simple and convenient unified formulation for calculating the axial compressive strength of both STCC columns and CFST columns is proposed for practical engineering applications.

On the coupled thermo-hydro-mechanical behaviors of layered porous media by the transformed differential quadrature method

In this paper, the thermo-hydro-mechanical (THM) problem of layered porous media is investigated by using the transformed differential quadrature method (TDQM). Starting from the THM governing equations in cylindrical coordinates, the partial differential equations in the transformed domain are obtained by using the Hankel integral transform. Then, the temporal domain and the spatial domain along depth are discretized according to the proposed TDQM, and the partial differential equations in the transformed domain are converted into algebraic equations at sampling points. By introducing load conditions, boundary conditions and continuity conditions, the matrix equation to solve the coupled THM problem of layered porous media is obtained. Finally, case studies are carried out to verify the TDQM solution, and to further discuss the influences of thermal and hydraulic parameters including the linear expansion coefficient of fluid and skeleton, permeable coefficient of fluid and porosity on the THM behaviors of layered porous media.

Nonlinear bending of unsymmetric double-layer lattice truss core sandwich beams

This paper studied the nonlinear bending of unsymmetric double-layer lattice truss core sandwich beams (LTCSBs). Five unsymmetric cases are considered by varying different materials and geometric thicknesses in two layers. To establish a theoretical model for the unsymmetric double-layer LTCSBs, Allen’s model and von Kármán nonlinear theory are employed. The present theoretical model is established by considering the midplane of the mid-sheet as the reference plane. Ritz method is applied to determine the deflection for the nonlinear bending, and verified by the finite element method (FEM). Finally, the effects of the loading direction, unsymmetric factors, and boundary conditions on the nonlinear bending behaviors of LTCSBs are studied. It is found that the nonlinear deflections of unsymmetric LTCSBs may exhibit softening-spring nonlinearity in one direction.

Buckling optimization of variable-stiffness composite plates via variable stiffness optimization algorithm

A variable stiffness optimization (VSO) algorithm is presented for optimizing variable-stiffness composite (VSC) plates with linear fiber path functions. A new definition of lamination parameters characterizing the distances between stacking configurations of VSC plates is presented. Using the inherent sensitivity of bending stiffness of composite laminates, the concept of “through thickness design” is introduced. The first step is to determine a good initial point for the VSC plates using three-dimensional sampling optimization (3DSO). The fiber angle design variables are then categorized into three groups. By optimizing the three groups' design variables sequentially and iteratively, the stiffness of the VSC plates is stiffened part by part until an optimum is reached. Lastly, the obtained optimum is redesigned accounting for the curvature constraint. The finite element method (FEM) is developed for the buckling analysis of VSC plates, and both Q4 and Q8 elements are employed to verify the accuracy and convergence of the FEM. Under a variety of boundary conditions and loading cases, FEM and VSO algorithm are used to maximize the buckling load of square and rectangular symmetrical VSC plates. Optimal results are compared with those available in the literature, demonstrating the effectiveness, robustness, and efficiency of the VSO algorithm.

Studying the mechanical properties of the mandible and injury prediction under the effect of ossification factors

Background and objectiveIt is essential to know the quantitative interactions between biological tissues and external mechanical and chemical stimuli. This assists the physicians to better know the quantitative behavior of the tissue and plan more effective therapy. In the literature, the effect of the chemical and mechanical loading was investigated on the bone biological cell activities and some mechanical features, but a lack of prediction of bone injury under the chemical and mechanical factors was sensed. Therefore, the present study aims to investigate the effects of the application of major chemical factors involved in ossification, including RANKL11Receptor Activator of Nuclear Factor Kappa Beta Ligand. (Receptor Activator of Nuclear Factor Kappa Beta Ligand), PTH22Parathyroid Hormone. (Parathyroid Hormone), and OPG33Osteoprotegerin. (Osteoprotegerin) on the mandibular bone biological osteoblast and osteoclast activities and mechanical properties. Moreover, the study assesses the bone injury possibility under uniform mastication pressure applied on the premolar tooth in terms of the mechanostat theory undergoing the effects of the chemical factors. MethodsA 3D geometry of the mandible-tooth assembly was generated from the CT image dataset. The geometry was next purified, solidified, and exported to FEM44Finite Element Method. (Finite Element Method) software to be meshed, where boundary conditions and loading were applied. Moreover, the mathematical system of differential equations to model the chemical factor effects on osteoblast and osteoclast activities as well as bone matrix volume fraction and elastic stiffness relations were applied. Next, the values of the equivalent strain were calculated to predict the injury states of the bone. ResultsThe results complied with the literature data. The results showed that RANKL and PTH increased the values of the equivalent strain from 450 με to 11500 με, while OPG reduced that from 450 με to 300 με. ConclusionsTherefore, RANKL and PTH doses of this study put the bone at risk of injury compared to the baseline of no dose applied, while OPG secured the bone from injury.

A new method for analyzing the thermomechanical behavior and the null point movement of energy piles

During heating or cooling, an energy pile elongates or shortens around the null point, where the thermally induced displacement is zero. Previously proposed computing methods typically require an initial null point assumption and iterations before calculating the thermomechanical response. We proposed a new method to directly calculate the thermomechanical response of energy piles based on the boundary shape function and load transfer approach, and we verified its feasibility by comparing the results with a field test. Then, this work investigated the effects of the pile head and tip restraint conditions, soil restraint, and thermal and initial mechanical load magnitudes on the thermomechanical response of energy piles through a series of case studies, particularly focusing on the interaction between the aforementioned influencing factors and the null point location. The analysis demonstrates that the position of the null point is primarily determined by the end restraint boundary conditions of the pile; however, changing the soil restraint and thermal load will cause the null point to move, and the direction and distance of the movement are related to the symmetry between the two extremity restraint conditions. Finally, changing the initial mechanical load also shifts the null point position.

Contact behaviors involving a nanobeam with surface effect by a rigid indenter

In this study, we present a novel surface model that utilizes surface energy density to predict the surface effect in nanobeam contact problems. To address the issue of a finite-length elastic nanobeam being indented by a rigid cylindrical indenter, we propose an equivalent substitution method. This method allows us to formulate analytical relations between the load and contact half-width for two different boundary cases. The explicit expressions of the contact-zone width, the pressure distribution in the contact zone, the deflection outside the contact zone, and the load–displacement relation are obtained for the nanobeam with surface effect and are compared with classical results in detail. The results show that the influence of the surface effect is very significant for nanobeam contact behavior, especially when the half-width of the contact zone increases and the contact zone becomes two independent symmetric strips. It is also found that the length-height ratio of nanobeam and the end support conditions have a fairly obvious effect on the normalized pressure distribution, which deviates significantly from the one predicted by the classical results due to the surface effect. However, for a given beam length and indenter radius, the ratio of the width of the contact zone to the beam thickness is almost constant, independent of the indenter load and beam boundary conditions. Meanwhile, the model predicts that the contact pressure distribution after the normalization of the average indentation pressure is almost independent of the indentation load and beam boundary conditions, but obviously depends on the surface effect parameters. The present method and result should be helpful not only to the measurement of mechanical properties of the indentation nanobeam but also to the design of the nanobeam-based devices.

A stabilized non-ordinary peridynamic model for linear piezoelectricity

Piezoelectric materials are used in a wide range of engineering applications as sensors, actuators, and transducers due to their intrinsic properties. However, analyzing these devices is not straightforward because of the material anisotropy and coupled electromechanical nature of the problems. In this study, a stabilized non-ordinary state-based peridynamic model for linear piezoelectricity is proposed. Fully coupled electromechanical simulation is conducted using an implicit method, and the tangent stiffness matrix is obtained via perturbation technique. Three two-dimensional electromechanical problems with combined static loading and various boundary conditions are used to validate the proposed technique. Then, the crack-opening displacements, and induced electric field on the crack-face are presented for a center-cracked PZT-5H plate. Hence, this study demonstrates that the proposed technique is capable of modeling linear piezoelectric materials and provides a promising method to study fracture and damage progression in piezoelectric materials.

Research on meso-equivalence simulation method of freeze–thaw concrete under multiaxial loading

In view of the influence of freeze–thaw cycles (FTCs) on the spatial strength of principal stress was not considered, a meso-equivalence simulation method was developed, considering the heterogeneous characteristics of FT concrete, to accurately depict frost damage behavior, which can be used to simulate the spatial strength distribution on principal stress of concrete with FTCs. Additionally, a meso-calculation method was employed to verify the loading boundary conditions and material constitutive models. Subsequently, the effectiveness of the meso-equivalence simulation method was established by its application to the mechanical analysis of FT concrete under multiaxial loads, alongside the formulation of meso-equivalence calculation models for FT-reinforced concrete (RC) beams. The results underscore the efficacy of the meso-calculation and meso-equivalence models in capturing damage mode within concrete, subjected to FTCs under multiaxial loads. Importantly, the strength envelope derived from the calculation model and the corresponding strength criterion for the multiaxial loading limit state of FTC-affected concrete aligns consistently with test findings. Moreover, the validation of the meso-equivalence simulation method is established by comparative analysis of the mechanical behavior of RC beams under FTCs, compared with test results, which not only enhances understanding of FT response but also contributes to the advancement of durability assessment.

Transition to turbulence in the wake of dandelion-like spoke disk

In order to solve the inevitable instability problem of dandelion-like unpowered aircraft, transient simulations are carried out for the transition to turbulence of the wake from stable to unstable stage under different Reynolds numbers, and the vortex mode characteristics presented by the vortex structure as the Reynolds number increases are identified. Furthermore, by monitoring the velocity and lift and drag coefficients at different positions in dandelion flow field, the spectral characteristics of flow velocity and aerodynamic coefficients in the turbulent phase triggered by extreme aerodynamic environment are revealed. Compared with solid disk, it is found that the bandgap structure is more conducive to expanding the stable flight threshold of the dandelion-like aircraft, that is, the canopy configuration has weakening effect on airflow fluctuations. In addition, an evaluation method for unsteady boundary Reynolds number and load capacity of a dandelion-like aircraft is presented. The proposed method aims to plan a reasonable number of filaments (or porosity) for further designing dandelion-like aircraft with flight stability and high load capacity under aerodynamic conditions at different Reynolds numbers.

How Linear Elastic Material Properties Affect Lung Tumor Motion and Deformation: A Finite Element Analysis

Radiation therapy (RT) is a common method for treating lung cancer; however, targeting the moving tumor while sparing the surrounding healthy lung tissue is challenging. One of the methods proposed is tracking the tumor at the time of treatment and using multi leaf collimators (MLCs) to precisely target the tumor shape. One of the most accurate ways to predict the position and shape of the tumor is simulating the respiratory process at the time of RT delivery. However, an efficient and accurate way to find patient-specific material characteristics of lung and tumor as input for the simulation is still to be found. In this work, we have i) studied the effect that lung and tumor material properties have on tumor displacement and deformation and ii) found out that a simple, linear, elastic model may be sufficient for examining the effect of the material properties on the tumor displacement and deformation. A model was constructed in a simulation environment. STL meshes of a lung and a tumor were imported and set up to have separate material property values assigned for elastic modulus, Poisson's ratio, and density. Boundary conditions on the lung included a fixed surface located at the top of the lung and a distributed boundary load on the lower surfaces of the lung. The boundary load provided a 2.5cm displacement of the lower surfaces to imitate the diaphragm motion during the inhalation phase of the breathing cycle. Lung density showed no effect on tumor movement or deformation. Tumor displacement differences as a function of material property values ranged from 0.0043-1.53cm. The lung elastic modulus had the greatest effect on tumor displacement, with displacements ranging from 0.041- 1.53cm, or a range of approximately 1.5cm. Lung Poisson's ratio values affected displacement with a maximum displacement range of 0.1942cm. Tumor elastic modulus showed an insignificant effect on displacement of the tumor, with displacement ranges up to 0.0043cm. Tumor displacement was also insensitive to tumor Poisson's ratio values with a maximum range of displacement of 0.0005cm. We found out that a simple, linear, elastic model was useful for examining the effect of the material properties on the tumor displacement and deformation. Tumor properties and Poisson's ratio of the lung did not affect the tumor displacement and deformation significantly; however, having a patient-specific approximated value for the lung elastic modulus is required for optimal modeling of the process. Implementation of MLC-based tracking in RT, although an effective technique, is complex and time-consuming. Finding simplifications that make this more cost- and time-efficient can potentially increase the accuracy of delivery techniques, especially for lung cancer. Improvements that can be easily adopted to the RT workflow can improve overall therapy outcomes and quality of life for more patients.

1D elastic viscoplastic consolidation analysis of bi‐layered soft ground under time‐dependent drainage boundary and ramp load

AbstractThe elastic viscoplastic properties are non‐negligible factors of clays that cause the deviation between the theoretical and the measured values, which were rarely incorporated in layered consolidation problems. Thus, this paper extended a generalized bi‐layered one‐dimensional (1D) consolidation model for soft ground under ramp load, simultaneously incorporating elastic viscoplastic deformation, non‐Darcy flow (NDF), and time‐dependent drainage boundary (TDB) condition. The finite volume technique was employed to numerically solve the control equation. Then, the proposed method solutions were verified by comparing with degenerated cases, including oedometer experimental results, analytical and semi‐analytical solutions with different boundary conditions. Furthermore, parametric studies were conducted on the bi‐layered clay creep consolidation characteristics by investigating the effect of the loading rate, interface and flow parameters, and the relative soil layer properties. The results demonstrate that the entire dissipation rate of the excess pore‐water pressure (EPWP) and settlement rate in the bi‐layered ground become faster as the soil thickness with high permeability or low compressibility increases. When considering the viscosity of soft clay, the EPWP exceeding the overlying construction load value can occur in poorly drained locations. Neglecting loading rate, time‐dependent drainage boundary (TDB), and NDF can result in a significant overestimation of consolidation and settlement proceedings.

Cyclic shear behavior of en-echelon joints under constant normal load

En-echelon joints occur widely in rock masses and are often subjected to dynamic loads during earthquakes and rock bursts, which considerably influence stability in rock engineering. However, little is known of the cyclic shear behavior of en-echelon joints. This study conducted a series of cyclic shear tests on en-echelon joints under constant normal load (CNL) boundary conditions to investigate the cyclic shear behavior and dilation characteristics. The results show that shearing mechanisms of en-echelon joints were determined by joint angles during cyclic shearing, leading to differences in the evolution of shear resistance and dilation characteristics. A new phenomenon was observed, in that, shear stresses increased and decreased with an increase in the number of cycles during small and large shear displacements, respectively. The shear strengths and average dilation angles under cyclic shear loads decreased with increasing number of cycles. The difference in the peak shear stresses between en-echelon joints with different joint angles decreased with the number of cycles (N). Finally, dilation only occurred in the first several cycles, contraction predominated after several cycles, and the contraction of the specimens at a positive angle was larger than that at a negative angle. These findings hold crucial implications for predicting surface ruptures after earthquakes.

Buckling analysis and optimization of variable angle tow composite plates via Ritz method and variable stiffness optimization

A novel variable stiffness optimization (VSO) algorithm is proposed accounting for the inherent mechanical characteristics of variable angle tow (VAT) plates. Through sampling in the design space of lamination parameters (LPs), a good initial point is identified in stacking sequence design domain. The concept of tailoring stiffness point by point through-thickness is then introduced. By using the linear fiber path function, design variables for VAT plates are divided into three groups, and then a layerwise optimization approach (LOA) is applied to optimize the angles from the outermost to the innermost stacking position within the three groups, sequentially and iteratively. Through a point-by-point optimization of fiber paths, the stiffness of VAT plates is enhanced part by part. Ritz-type buckling solutions are presented for VAT composite plates with arbitrary boundary conditions. Using first-order shear deformation theory (FSDT), the translational and rotational degrees of freedom of the plate are divided into in-plane and out-of-plane components to solve the prebuckling and buckling problems independently. Buckling loads of VAT plates are optimized under multiple boundary conditions and loadings. Results indicate that VSO algorithm is efficient and robust, and the buckling resistance capacity of optimized VAT plates can be improved approximately twice over constant-stiffness laminates.

Limit load and failure mechanisms of a vertical Hoek-Brown rock slope

The problem considered in this short note is the limit load determination of a vertical rock slope. The classical limit theorem is employed with the use of adaptive finite elements and nonlinear programming to determine upper and lower bound limit loads of a Hoek-Brown vertical rock slope. The objective function of the mathematical programming problem is such as to optimize a boundary load, which is known as the limit load, resembling the ultimate bearing capacity of a strip footing. While focusing on the vertical slope, parametric studies are carried out for several dimensionless ratios such as the dimensionless footing distance ratio, the dimensionless height ratio, and the dimensionless rock strength ratio. A comprehensive set of design charts is presented, and failure envelopes shown with the results explained in terms of three identified failure mechanisms, i.e. the face, the toe, and the Prandtl-type failures. These novel results can be used with great confidence in design practice, in particularly noting that the current industry-based design procedures for the presented problem are rarely found.

Mechanical behavior of round bamboo under transverse local compression

Bamboo is a material with low transverse mechanical properties. To study the mechanical behavior of round bamboo under transverse local compression, 60 round bamboo culms were subjected to three-point bending tests. The effects of different parameters on the transverse local compressive behavior were investigated experimentally. Finally, the transverse local compressive ultimate bearing capacity of round bamboo was estimated using prediction equations. The results indicated that under three load boundary conditions, axial cracks appeared on both sides of the specimens in the midspan region, dents of different sizes appeared at the loading points, and additional fractures occurred in the inner diaphragms of the specimens with the loading point at the node. The specimens subjected to point and line loads underwent brittle failure. Under the space-curve load, the specimens with a loading point at the internode exhibited ductile failure, whereas the specimens with a loading point at the node exhibited brittle failure. To obtain a favorable transverse local compressive ultimate bearing capacity, it was optimal to consider the space-curve load as the load boundary condition and position the transverse local compression at the bamboo node. The results of the prediction equations agreed well with the test results.

Mechanical calculation of elastic folding of a thin-walled deployable composite boom for space applications

The paper investigates the stress–strain state of a thin-walled deployable N-shaped composite boom during elastic folding. A finite element model using ANSYS 2021 R2 software (explicit formulation) is developed, considering boundary conditions, loads, and analysis parameters. Numerical calculations are performed for various cylindrical mandrel radii, revealing a strong dependence on maximum stress on the mandrel radius. Results indicate reliable folding without damage for a mandrel radius of 20 mm or more. This study solves the complex problem of modeling elastic folding, providing essential information for engineers to achieve an optimal design.

Development and Improvement of Numerical Models of Welded Joints with Multiple Defects

This paper presents the development of numerical models which were used to simulate the behaviour of welded joints containing different combinations of multiple defects under tensile loads. Four representative combinations of defects were selected (including undercuts, incomplete root penetration, misalignments...), based on practical experience. In order to create accurate and functional models, this research involve a number of stages. This paper will focus on the various improvements made to the models, which started in relatively simple form. For this purpose, initial experimental and numerical analyses were carried out on specimens made of low-alloyed low-carbon steel S235, and after their accuracy was verified, the same methodology was applied to specimens made of higher quality material, steel S275. Improvements made to the models involved geometry, different combinations of boundary conditions and loads, and some were based on stress-strain states obtained by a combination of tensile testing and digital image correlation. The final result was a set of detailed numerical models which accurately simulated the behaviour of welded joints with multiple defects in them.

Consolidation of multilayered soil with fractional derivative viscoelasticity due to surface loading and internal pumping

Classical Terzaghi’s solution provides a useful tool to predict the one-dimensional consolidation of homogeneous elastic soil layer with fully drained/undrained boundary condition under instantaneous loading. Due to the sedimentation process and complex internal structure, natural soils usually exhibit multilayered inhomogeneity and viscoelastic behavior. In practical cases, the drainage capacity of the boundaries can change with time. Thus, these practical factors should be well in considered for accurate prediction of the consolidation. This paper extends the classical Terzaghi’s solution to multilayered viscoelastic soil with continuous drainage boundaries and subjected to time dependent loading. The fractional derivative Kelvin-Voigt model is used to describe the viscoelasticity of soil. Two loading cases namely surface loading and internal pumping are considered. The consolidation problem is solved by Laplace transform technique and a transfer matrix formulation. Analytical solutions for excess pore water pressure, effective stress and settlement are given. The present solution is general and can reduce to existing solutions available in the literatures. Numerical studies are conducted to investigate the effects of viscoelastic parameters, boundary drainage capacity and loading rate on the consolidation behavior. It is shown that the multilayered soil system with large viscosity coefficient and small fractional order can consolidate fast. For the consolidation due to internal pumping, the drainage parameters have no influence on the consolidation process.

Analysis of Moderately Thick Functionally Graded Plates Subjected to Transverse Loads

In the present work, flexural analysis of a thin to moderately thick FGM plate subjected to transverse loads have been studied using finite element method. The formulation is developed based on the First order Shear Deformation Theory (FSDT). The mechanical properties are assumed to vary continuously through the thickness of the plate and obey a power law distribution of the volume fraction of the constituents. FGM’s are typically heterogeneous in nature and a homogenization scheme is generally adopted for the analysis. To ascertain the effect of homogenization schemes on the material properties, the variation of volume fraction through the thickness have been computed using two different material homogenization techniques; namely the Rule of Mixtures and Mori-Tanaka scheme. In calculating the effective material properties through the thickness numerical integration have been used to evaluate the integrals which is easier and faster when compared to symbolic integration. A detailed discussion comparing the results from both the homogenization schemes have been presented. In addition to that a detailed parametric study bringing out the effect of boundary conditions, loading intensities and volume fraction index have been presented. Convergence tests and comparison studies have been carried out to demonstrate the efficiency of the present formulation.