• Advances in materials Research
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• v.11 no.3
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• pp.171-190
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• 2022

In this paper, the problem of interfacial stresses in steel cantilever beams strengthened with bonded composite laminates is analyzed using linear elastic theory. The analysis is based on the deformation compatibility approach, where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. The original study in this paper carried out an analytical solution to estimate shear and peel-off stresses, as, interfacial stress analysis concentration under the uniformly distributed load and shear lag deformation. The theoretical prediction is compared with authors solutions from numerous researches. This phenomenon of deformation of the members, which gives probably approach on the study of interface of the reinforced structures, is called "shear lag effect". The resolution in this paper shows that the shear stress and the normal stress are significant and, are concentrated at the end of the composite plate of reinforcement, called "edge effect". A parametric study is carried out to show the effects of the variables of design and the physical properties of materials. This research is helpful for the understanding on mechanical behaviour of the interface and design of such structures.

• Steel and Composite Structures
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• v.25 no.2
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• pp.157-175
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• 2017

The novelty of this work is the use of a new displacement field that includes undetermined integral terms for analyzing thermal buckling response of functionally graded (FG) sandwich plates. The proposed kinematic uses only four variables, which is even less than the first shear deformation theory (FSDT) and the conventional higher shear deformation theories (HSDTs). The theory considers a trigonometric variation of transverse shear stress and verifies the traction free boundary conditions without employing the shear correction factors. Material properties of the sandwich plate faces are considered to be graded in the thickness direction according to a simple power-law variation in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are assumed as uniform, linear and non-linear temperature rises within the thickness direction. An energy based variational principle is employed to derive the governing equations as an eigenvalue problem. The validation of the present work is checked by comparing the obtained results the available ones in the literature. The influences of aspect and thickness ratios, material index, loading type, and sandwich plate type on the critical buckling are all discussed.

• Steel and Composite Structures
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• v.26 no.4
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• pp.473-484
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• 2018

Free vibration of cross-ply laminated plates using a higher-order shear deformation theory is studied. The arbitrary number of layers is oriented in symmetric and anti-symmetric manners. The plate kinematics are based on higher-order shear deformation theory (HSDT) and the vibrational behaviour of multi-layered plates are analysed under simply supported boundary conditions. The differential equations are obtained in terms of displacement and rotational functions by substituting the stress-strain relations and strain-displacement relations in the governing equations and separable method is adopted for these functions to get a set of ordinary differential equations in term of single variable, which are coupled. These displacement and rotational functions are approximated using cubic and quantic splines which results in to the system of algebraic equations with unknown spline coefficients. Incurring the boundary conditions with the algebraic equations, a generalized eigen value problem is obtained. This eigen value problem is solved numerically to find the eigen frequency parameter and associated eigenvectors which are the spline coefficients.The material properties of Kevlar-49/epoxy, Graphite/Epoxy and E-glass epoxy are used to show the parametric effects of the plates aspect ratio, side-to-thickness ratio, stacking sequence, number of lamina and ply orientations on the frequency parameter of the plate. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• Advances in nano research
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• v.7 no.6
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• pp.443-457
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• 2019

In this investigation, dynamic and bending behaviors of isolated protein microtubules are analyzed. Microtubules (MTs) can be considered as bio-composite structures that are elements of the cytoskeleton in eukaryotic cells and posses considerable roles in cellular activities. They have higher mechanical characteristics such as superior flexibility and stiffness. In the modeling purpose of microtubules according to a hollow beam element, a novel single variable sinusoidal beam model is proposed with the conjunction of modified strain gradient theory. The advantage of this model is found in its new displacement field involving only one unknown as the Euler-Bernoulli beam theory, which is even less than the Timoshenko beam theory. The equations of motion are constructed by considering Hamilton's principle. The obtained results are validated by comparing them with those given based on higher shear deformation beam theory containing a higher number of variables. A parametric investigation is established to examine the impacts of shear deformation, length scale coefficient, aspect ratio and shear modulus ratio on dynamic and bending behaviors of microtubules. It is remarked that when length scale coefficients are almost identical of the outer diameter of MTs, microstructure-dependent behavior becomes more important.

• Smart Structures and Systems
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• v.29 no.3
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• pp.395-420
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• 2022

A new hybrid quasi-3D and 2D high-order shear deformation theory is studied in this mathematical formulation, for an investigation of the bending, free vibrations and buckling influences on a functionally graded material plate. The theoretical formulation has been begun by a displacement field of five unknowns, governing the transverse displacement across the thickness of the plate by bending, shearing and stretching. The transverse shear deformation effect has been taken into consideration, satisfying the stress-free boundary conditions, especially on plate free surfaces as parabolic variation through its thickness. Thus, the mechanical properties of the functionally graded plate vary across the plate thickness, following three distributions forms: the power law, exponential form and the Mori-Tanaka scheme. The mechanical properties are used to develop the equations of motion, obtained from the Hamilton principle, and solved by applying the Navier-type solution for simply supported boundary conditions. The results obtained are compared with other solutions of 2D, 3D and quasi-3D plate theories have been found in the literature.

• Advances in concrete construction
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• v.17 no.2
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• pp.75-92
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• 2024

High Strength steel reinforced Reactive Powder Concrete (RPC) Beam is a new type of beams which has evident advantages than the conventional concrete beams. However, there is limited research on the shear bearing capacity of high-strength steel reinforced RPC structures, and there is a lack of theoretical support for structural design. In order to promote the application of high-strength steel reinforced RPC structures in engineering, it is necessary to select a shear model and derive applicable calculation methods. By considering the shear span ratio, steel fiber volume ratio, longitudinal reinforcement ratio, stirrup ratio, section shape, horizontal web reinforcement ratio, stirrup configuration angle and other variables in the shear test of 32 high-strength steel reinforced RPC beams, the applicability of three theoretical methods to the shear bearing capacity of high-strength steel reinforced RPC beams was explored. The plasticity theory adopts the RPC200 biaxial failure criterion, establishes an equilibrium equation based on the principle of virtual work, and derives the calculation formula for the shear bearing capacity of high-strength steel reinforced RPC beams; Based on the Strut and Tie Theory, considering the softening phenomenon of RPC, a failure criterion is established, and the balance equation and deformation coordination condition of the combined force are combined to derive the calculation formula for the shear bearing capacity of high-strength reinforced RPC beams; Based on the Rankine theory and Rankine failure criterion, taking into account the influence of size effects, a calculation formula for the shear bearing capacity of high-strength reinforced RPC beams is derived. Experimental data is used for verification, and the results are in good agreement with a small coefficient of variation.

• Structural Engineering and Mechanics
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• v.36 no.5
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• pp.625-642
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• 2010

The Integrated Force Method (IFM) is a novel matrix formulation developed for analyzing the civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. This paper presents a new 12-node serendipity quadrilateral plate bending element MQP12 for the analysis of thin and thick plate problems using IFM. The Mindlin-Reissner plate theory has been employed in the formulation which accounts the effect of shear deformation. The performance of this new element with respect to accuracy and convergence is studied by analyzing many standard benchmark plate bending problems. The results of the new element MQP12 are compared with those of displacement-based 12-node plate bending elements available in the literature. The results are also compared with exact solutions. The new element MQP12 is free from shear locking and performs excellent for both thin and moderately thick plate bending situations.

• Structural Engineering and Mechanics
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• v.17 no.5
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• pp.641-654
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• 2004

This paper presents a theoretic model of a smart structure, a transversely isotropic piezoelectric thick square plate constructed with three laminas, piezoelectric-elastic-piezoelectric layer, by adopting the first order shear deformation plate theory and piezoelectric theory. This model assumes that the transverse displacements through thickness are linear, and the in-plane displacements in the mid-plane of the plate are not taken to be account. By using Fourier's series expansion, an exact Navier typed analytical solution for deflection and electric potential of the simply supported smart plate is obtained. The electric boundary conditions are being grounded along four vertical edges. The external voltage and non-external voltage applied on the surfaces of piezoelectric layers are all considered. The convergence of the present approach is carefully studied. Comparison studies are also made for verifying the accuracy and the applicability of the present method. Then some new results of the electric potentials and displacements are provided. Numerical results show that the electrostatic voltage is approximately linear in the thickness direction, while parabolic in the plate in-plane directions, for both the deflection and the electric voltage. These results are very useful for distributed sensing and finite element verification.

• Steel and Composite Structures
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• v.26 no.1
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• pp.89-102
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• 2018

This work investigates a novel plate formulation and a modified couple stress theory that introduces a variable length scale parameter is presented to discuss the static and dynamic of functionally graded (FG) micro-plates. A new type of third-order shear deformation theory of Reddy that use only 4 unknowns by including undetermined integral variables is proposed in this study. The equations of motion are derived from Hamilton's principle. Analytical solutions are obtained for a simply supported micro-plate. Numerical examples are presented to examine the effect of the length scale parameter on the responses of micro-plates. The obtained results are compared with the previously published results to demonstrate the correctness of the present formulation.

• Smart Structures and Systems
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• v.21 no.1
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• pp.75-97
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• 2018

In this paper, a novel higher-order shear deformation theory (HSDT) is proposed for the analysis of the hygro-thermo-mechanical behavior of functionally graded (FG) plates resting on elastic foundations. The developed model uses a novel kinematic by considering undetermined integral terms and only four variables are used in this model. The governing equations are deduced based on the principle of virtual work and the number of unknown functions involved is reduced to only four, which is less than the first shear deformation theory (FSDT) and others HSDTs. The Navier-type exact solutions for static analysis of simply supported FG plates subjected to hygro-thermo-mechanical loads are presented. The accuracy and efficiency of the present model is validated by comparing it with various available solutions in the literature. The influences of material properties, temperature, moisture, plate aspect ratio, side-to-thickness ratios and elastic coefficients parameters on deflections and stresses of FG plates are also investigated.