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CONTENTS
Volume 76, Number 4, November25 2020
 

Abstract
This work presents the formulation of the isogeometric collocation method to solve the strong form equation of a unified and integrated approach of Reissner Mindlin plate theory (UI-RM). In this plate theory model, the total displacement is expressed in terms of bending and shear displacements. Rotations, curvatures, and shear strains are represented as the first, the second, and the third derivatives of the bending displacement, respectively. The proposed formulation is free from shear locking in the Kirchhoff limit and is equally applicable to thin and thick plates. The displacement field is approximated using the B-splines functions, and the strong form equation of the fourth-order is solved using the collocation approach. The convergence properties and accuracy are demonstrated with square plate problems of thin and thick plates with different boundary conditions. Two approaches are used for convergence tests, e.g., increasing the polynomial degree (NELT = 1✕1 with p = 4, 5, 6, 7) and increasing the number of element (NELT = 1✕1, 2✕2, 3✕3, 4✕4 with p = 4) with the number of control variable (NCV) is used as a comparable equivalent variable. Compared with DKMQ element of a 64✕64 mesh as the reference for all L/h, the problem analysis with isogeometric collocation on UI-RM plate theory exhibits satisfying results.

Key Words
unified and integrated Reissner-Mindlin; isogeometric analysis; B-spline; collocation method

Address
Department of Civil Engineering, Universitas Indonesia, Depok 16424, Indonesia

Abstract
In this paper, a new semi-analytical solution for estimating the pull-in parameters of electrically actuated functionally graded (FG) nanobeams is proposed. All the bulk and surface material properties of the FG nanoactuator vary continuously in thickness direction according to power law distribution. Here, the modified couple stress theory (MCST) and Gurtin-Murdoch surface elasticity theory (SET) are jointly employed to capture the size effects of the nanoscale beam in the context of Euler-Bernoulli beam theory. According to the MCST and SET and accounting for the mid-plane stretching, axial residual stress, electrostatic actuation, fringing field, and dispersion (Casimir or/and van der Waals) forces, the nonlinear nonclassical equation of motion and boundary conditions are obtained derived using Hamilton principle. The proposed semi-analytical solution is derived by employing Galerkin method in conjunction with the Particle Swarm Optimization (PSO) method. The proposed solution approach is validated with the available literature. The freestanding behavior of nanoactuators is also investigated. A parametric study is conducted to illustrate the effects of different material and geometrical parameters on the pull-in response of cantilever and doubly-clamped FG nanoactuators. This model and proposed solution are helpful especially in mechanical design of micro/nanoactuators made of FGMs.

Key Words
semi-analytical solution; pull-in instability; freestanding behavior; FG nanobeams; integrated couple stress-surface energy model

Address
Mohamed A. Attia: Mechanical Design and Production Dept., Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt
Rasha M. Abo-Bakr: Deptartment of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt

Abstract
This paper presents an investigation on the dynamic behavior of SRC columns with built-in cross-shaped steels under impact load. Seven 1/2 scaled SRC specimens were subjected to low-speed impact by a gravity drop hammer test system. Three main parameters, including the lateral impact height, the axial compression ratios and the stirrup spacing, were considered in the response analysis of the specimens. The failure mode, deformation, the absorbed energy of columns, as well as impact loads are discussed. The results are mainly characterized by bending-shear failure, meanwhile specimens can maintain an acceptable integrity. More than 33% of the input impact energy is dissipated, which demonstrates its excellent impact resistance. As the impact height increases, the flexural cracks and shear cracks observed on the surface of specimens were denser and wider. The recorded time-history of impact force and mid-span displacement confirmed the three stages of relative movement between the hammer and the column. Additionally, the displacements had a notable delay compared to the rapid changes observed in the measured impact load. The deflection of the mid-span did not exceed 5.90mm while the impact load reached peak value. The impact resistance of the specimen can be improved by proper design for stirrup ratios and increasing the axial load. However, the cracking and spalling of the concrete cover at the impact point was obvious with the increasing in stiffness.

Key Words
Steel Reinforced Concrete (SRC) column; cross-shaped steel skeleton; lateral impact; experiment study; dynamic response; failure mode

Address
School of Urban Construction, Yangtze University, Jingzhou 434023, China

Abstract
This paper proposed a novel form of reinforced concrete (RC) shear wall confined with boundary columns. The structural effect of applying steel fiber reinforced concrete (SFRC) in the wall-column systems was studied. Three full-scale wall samples were constructed including two RC wall-RC column samples with different stirrup ratios and one RC wall-SFRC column sample. Low frequency cyclic testing was carried out to investigate the failure modes, hysteretic behavior, load-bearing capacity, ductility, stiffness degradation and energy dissipation. ABAQUS models were set up to simulate the structural behavior of tested samples, and good agreement was achieved between numerical simulation and experimental results. A further supplementary parametric study was conducted based on ABAQUS models. Both experimental and numerical results showed that increasing stirrup ratio in boundary columns did not affect much on load bearing capacity or stiffness degradation of the system. However, applying SFRC in boundary columns showed significant enhancement on load bearing capacity. Numerical simulation also shows that the structural performances of RC wall-SFRC column system were comparable to a wall-column system fully with SFRC.

Key Words
shear wall; steel-fiber reinforced concrete; cyclic tests; ABAQUS model; boundary columns

Address
Liusheng Chu, Yuexi He, Zhanqi Cheng: School of Civil Engineering, Zhengzhou University, Zheng Zhou, Henan Province, China
Danda Li, Xing Ma: UniSA STEM, University of South Australia, Adelaide, SA, Australia

Abstract
This study extends previous experimental research on the shear behaviour of macrosynthetic fibre-reinforced concrete beams and compares them to steel fibre-reinforced concrete beams with similar mechanical and geometrical properties. This work employed two fibre types: 60/0.9 (long/diameter) double hooked-end steel fibre and 60/85 monofilament polypropylene fibre. Beams were tested by shear loading covering parameters, such as two different cross-section widths, two shear-span-to-effective-depth ratios, two fibre types and using repetitions with and without transverse reinforcement. For quantitative comparison purposes, crack pattern evolution was studied along increasing loads levels. Effects were studied by photogrammetry, including influence of fibres on crack propagation in uncracked and dowel zones, influence of fibres on stirrup behaviour, and shear deformation or kinematics of critical shear cracks. The results evidenced similar effectiveness for both fibre types in controlling shear crack propagation and horizontal dowel cracking. Both fibres provided similar shear ductility and shear deflections. Consequently, the authors confirm that residual flexural tensile strengths are a convenient parameter for characterising the shear behaviour of fibre-reinforced concrete beams.

Key Words
fibre-reinforced concrete; shear-critical beams; macrosynthetic fibres; shear strength

Address
Instituto de Ciencia y Tecnología del Hormigón (ICITECH), Universitat Politècnica de Valencia, Camino de Vera s/n, 46022, Valencia, Spain

Abstract
This paper presents an error estimation technique for 2-D crack analysis by an enriched natural element (more exactly, enriched Petrov-Galerkin NEM). A bare solution was approximated by PG-NEM using Laplace interpolation functions. Meanwhile, an accurate quasi-exact solution was obtained by a combined use of enriched PG-NEM and the global patch recovery. The Laplace interpolation functions are enriched with the near-tip singular fields, and the approximate solution obtained by enriched PG-NEM was enhanced by the global patch recovery. The quantitative error amount is measured in terms of the energy norm, and the accuracy (i.e., the effective index) of the proposed method was evaluated using the errors which obtained by FEM using a very fine mesh. The error distribution was investigated by calculating the local element-wise errors, from which it has been found that the relative high errors occurs in the vicinity of crack tip. The differences between the enriched and non-enriched PG-NEMs have been investigated from the effective index, the error distribution, and the convergence rate. From the comparison, it has been justified that the enriched PG-NEM provides much more accurate error information than the non-enriched PG-NEM.

Key Words
crack analysis; error estimation; natural element method; interpolation enrichment; stress recovery; global and local errors

Address
Department of Naval Architecture and Ocean Engineering, Hongik University, Sejong 30016, Korea

Abstract
This paper presents the results of an experimental study on the residual behavior of reinforced recycled aggregate concrete (RRAC) beam-columns after exposure to elevated temperatures. Two parameters were considered in this test: (a) recycled coarse aggregate (RCA) replacement percentages (i.e. 0, 30, 50, 70 and 100%); (b) high temperatures (i.e. 20, 200, 400, 600, and 800℃). A total of 25 RRAC short columns and 32 RRAC beams were conducted and subjected to different high temperatures for 1 h. After cooling down to ambient temperature, the following basic physical and mechanical properties were then tested and discussed: (a) surface change and mass loss ratio; (b) strength of recycled aggregate concrete (RAC) and steel subjected to elevated temperatures; (c) bearing capacity of beam-columns; (d) load-deformation curve. According to the test results, the law of performance degradation of RRAC beam-columns after exposure to high temperatures is analyzed. Finally, introducing the influence coefficient of RCA replacement percentage and high temperatures, respectively, to correct the calculation formulas of bearing capacity of beam-columns in Chinese Standard, and then the residual bearing capacity of RRAC beam-columns subjected elevated temperatures is calculated according to the modified formulas, the calculated results are in good agreement with the experimental results.

Key Words
reinforced recycled aggregate concrete (RRAC); beam-columns; elevated temperatures; performance degradation; residual bearing capacity

Address
Zongping Chen, Ji Zhou, Ying Liang and Peihuan Ye: College of Civil Engineering and Architecture, Guangxi University, 530004 Nanning, P.R. China.
Zongping Chen: Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, Guangxi University, Nanning 530004,Guangxi, P.R. China

Abstract
Concurrent topology optimization of macrostructure and microstructure has attracted significant interest due to its high structural performance. However, most of the existing works are carried out under deterministic conditions, the obtained design may be vulnerable or even cause catastrophic failure when the load position exists uncertainty. Therefore, it is necessary to take load position uncertainty into consideration in structural design. This paper presents a computational method for robust concurrent topology optimization with consideration of load position uncertainty. The weighted sum of the mean and standard deviation of the structural compliance is defined as the objective function with constraints are imposed to both macro- and micro-scale structure volume fractions. The Bivariate Dimension Reduction method and Gauss-type quadrature (BDRGQ) are used to quantify and propagate load uncertainty to calculate the objective function. The effective properties of microstructure are evaluated by the numerical homogenization method. To release the computation burden, the decoupled sensitivity analysis method is proposed for microscale design variables. The bi-directional evolutionary structural optimization (BESO) method is used to obtain the black-and-white designs. Several 2D and 3D examples are presented to validate the effectiveness of the proposed robust concurrent topology optimization method.

Key Words
load position uncertainty; robust concurrent topology optimization; homogenization method; Bivariate Dimension Reduction method; Gauss-type quadrature

Address
Jinhu Cai: School of Mechanical Engineering and Automation, Beihang University, Beijing, China
Chunjie Wang : State Key Laboratory of Virtual Reality and Systems, Beihang University, Beijing, China

Abstract
As a new type of concrete material, basic magnesium sulfate cement concrete (BMSC) has the advantages, such as early strength, high strength, good toughness and crack resistance. However, it is unclear about the degradation of the mechanical properties of BMSC columns, which is exposed to the natural environment for several years. In order to apply this new concrete to practical engineering, six large-eccentricity compressive columns of BMSC were studied. The mechanical properties such as the crack propagation, failure morphology, lateral displacement and bearing capacity of BMSC column were studied. The results show that the degradation rate of ultimate load of BMSC column is from 6% to 7%. The degradation rate of the stiffness of the column is from 6% to 13%. With the increase of compressive strength of BMSC, the axial displacement and lateral displacement are gradually reduced. The calculation model of bearing capacity of the BMSC column under the large eccentric compression is proposed. This paper provides a reference for the application of BMSC columns in the civil engineering.

Key Words
basic magnesium sulfate cement concrete (BMSC); column; natural environment; steel corrosion; large eccentric compression; crack; bearing capacity; stiffness

Address
Department of Civil Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China

Abstract
On the basis of nonlocal strain gradient theory, considering the material properties of porous FGM changing with thickness and the influence of moment of inertia, the wave equation of FG nano circular plate is derived by using the first-order shear deformation plate theory, by introducing dimensionless parameters, we transform the equations into dimensionless wave equations, and the dispersion relations of bending wave, shear wave and longitudinal wave are obtained by Laplace and Hankel integral transformation method. The influence of nonlocal parameter, porosity volume fraction, strain gradient parameters and power law index on the propagation characteristics of bending wave, shear wave and longitudinal wave in FG nano circular plate.

Key Words
flexural wave; shear wave; longitudinal wave; circular nanoplate; nonlocal strain gradient theory

Address
Wubin Shan, Zulu Deng, Hao Zhong, Hu Mo,
Ziqiang Han, Zhi Yang, Chengyu Xiang, Shuzhou Li: Hunan Electrical College of Technology, School of elevator engineering, Xiangtan 411100, China
Wubin Shan: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China
Peng Liu: School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin, 541004, China


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