The Journal of Solid Mechanics (JSM) is a quarterly journal which is dedicated to the publication of original and peer-reviewed papers relating to the mechanics of solids and structures. This influential publication covers a broad area of mechanical engineering activities associated with the classical problems of structural analysis to mechanics of solids, fracture mechanics, heat transfer, thermal effects in solids, optimum design methods, and numerical techniques. This journal is fully open access and provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. Publisher: Islamic Azad University, Co-publishing, OICC Press, UK Journal Owner: Islamic Azad University
Buckling Analysis of Functionally Graded Materials of Thin Rectangular Plates Applying the Modified Differential Quadrature Method
This study investigates the buckling behavior of thin rectangular plates composed of Functionally Graded Materials (FGMs) using the Modified Differential Quadrature Method (MDQM). Through the application of this method, the governing differential equations are transformed into a system of linear algebraic equations suitable for buckling analysis. After defining the relevant parameters, the problem formulation enables the computation of buckling coefficients. The buckling response of the plates under compressive loading is examined for various boundary conditions, and the influence of fixed boundary effects on the resulting buckling coefficients is analyzed. The results obtained using the MDQM are compared with corresponding analytical solutions and finite element analysis outcomes. The comparisons demonstrate that the proposed approach effectively predicts the buckling loads of rectangular plates under different boundary conditions. It is also observed that the accuracy of the results is highly sensitive to the number of grid points employed; insufficient grid density leads to non-convergent solutions, indicating that careful discretization is essential for reliable application of the MDQM. Furthermore, the buckling coefficient is shown to vary significantly with boundary conditions. Overall, the close agreement between MDQM results and finite element data confirms the suitability of the method for analyzing the buckling behavior of non-uniform plates.
Copyright (c) 2026 Reza Kazemi, Mohsen Rafiei Karahroudi, Seyed Alireza Mousavi Shirazi (Author) https://creativecommons.org/licenses/by/4.0
Seismic Loss Assessment of RC Structures Rehabilitated by Viscous Dampers Designed Based on Performance Index Method
This study aims to evaluate and compare the behavior of viscous dampers designed using the Performance Index (PI) method and the ASCE7 approach. To this end, two categories of 12-story reinforced concrete (RC) moment-resisting frames are considered in this study: standard and substandard structures. The substandard structure is rehabilitated by viscous dampers. Although the PI method is typically utilized in designing Pall friction dampers, in this study, the approach recommended by ASCE7 and the energy-based PI method is employed in designing viscous dampers. Initially, various performance parameters of the structures are compared. The results have demonstrated that lateral displacement and roof acceleration values are lower in the ASCE7 approach than in the PI method. However, the structure equipped with viscous dampers designed via the PI method exhibits lower drift and dissipated plastic strain energy compared to the ASCE7 approach. Then, using Incremental Dynamic Analysis (IDA), fragility and loss function curves are obtained and presented for the three considered structural configurations. The findings revealed that the structure with dampers designed by the PI method has a lower probability of exceedance at a given spectral acceleration compared to other structures. Furthermore, the loss function based on the FEMA P-58 methodology indicates that, at the design spectral acceleration, the repair-to-construction cost ratio at the probability of 50% is 0.45 for structures without dampers, and 0.07 and 0.08 for those with dampers designed using the PI and ASCE7 methods, respectively.
Copyright (c) 2025 Hamed Poloee Amirabad, Sepideh Rahimi, Mohamad Hoseinzadeh, Morteza Hosseinali Beygi (Author) https://creativecommons.org/licenses/by/4.0
Length Scale Dependency of Micropolar Equations of Elasticity in Hollow Cylinder Subjected to Mechanical Load
This paper performs a numerical analysis of the stress behavior of a hollow cylinder within the framework of micropolar elasticity, taking explicitly into account length-scale effects. The governing field equations are established in polar coordinates, where size dependence is captured through characteristic material length parameters and the formulation is given in terms of stress functions. The resulting boundary value problem is then solved by using the Generalized Differential Quadrature (GDQ) technique. The obtained numerical results clearly show a strong dependency of the stress response from the material length parameter. Indeed, increasing the latter from ????=0 the value corresponding to the classical elasticity model-to the considered micrometer scale value, the maximum values of radial and circumferential stresses decrease by about 46% and 45%, respectively, whereas the maximum value of couple stress mrθ decreases by about 30%. These findings are particularly relevant for micro-scale engineering applications such as MEMS devices and biomedical implants, where component dimensions approach the material's micro-structural scale and classical elasticity proves inadequate. Furthermore, the pronounced size effects observed at the inner radius where stress gradients are highest highlight the critical need for micropolar theory in accurate stress analysis of microscale cylindrical structures. This work provides a foundation for future research on functionally graded micropolar materials and establishes GDQ as an efficient computational tool for capturing intricate size-effects in advanced micro-structured components.
Generalized Differential Quadrature Method (GDQM)
Copyright (c) 2025 Ameer Khalaf Ali, Mohsen Jabbari, Seyed Mahdi Khorsandijou (Author) https://creativecommons.org/licenses/by/4.0
A Comparative Assessment of DF2016 and MMC3Fracture Criteria for Predicting Crack Initiation inSingle Point Incremental Forming
Accurately predicting fracture remains a significant challenge in single point incremental forming (SPIF) due to the complex and inherently nonlinear loading paths. This study presents a comparative evaluation of two advanced ductile fracture criteria, DF2016 and the modified Mohr-Coulomb (MMC3), for predicting crack initiation in SPIF of AA1050 aluminum sheets. The fracture models were calibrated using tensile tests and implemented in Abaqus/Explicit 2022 via a VUSDFLD user subroutine, coupled with a Swift-Voce hardening law. Numerical models were validated by comparing simulated thickness distributions and in-plane strains against experimental data from truncated conical and pyramidal specimens with variable wall angle. To account for the non-proportional loading characteristic of SPIF, a nonlinear damage accumulation rule, calibrated using the straight groove test, was incorporated to improve prediction precision. The results indicate that both criteria successfully predict the onset depth and location of cracks, demonstrating good agreement with experimental observations. However, the DF2016 criterion exhibited superior accuracy over MMC3, attributed to its enhanced capability to capture a wider range of deformation modes.
Copyright (c) 2026 Seyed Amin Teymouri Sendesi, Mohammad Mehdi Kasaei, Majid Majidi, Seyed Jalal Hashemi (Author) https://creativecommons.org/licenses/by/4.0
Finite Element Evaluation of Stress Distribution in the Buried Steel Pipelines in Presence of Polyethylene Coating
Stress analysis of buried pipes is essential for safety, longer life, and prevention of structural failures. The present research work is related to the stress analysis in the gas transmission steel pipeline buried in the soil. The steel pipe has a three-layer polyethylene coating with viscoelastic properties. The stresses are caused by traffic loads, including the passage of vehicles on the surface, soil weight and fluid pressure inside the pipe. The stress analysis on the buried pipe for three different states including (I) static loading- pipe without coating, (II) static loading- pipe with viscoelastic coating, and (III) dynamic loading- pipe with viscoelastic coating have been performed using finite element method. The results of numerical modeling in ANSYS for static loading and uncoated pipe have been compared with the theoretical outcomes and the accuracy of the modeling has been confirmed. Based on the obtained observations, the dynamic loading and viscoelastic coating were able to affect the stress distribution created in the buried pipe, in comparison with the static loading without coating. Also, increasing the friction in the pipe-soil interface kept the tensile stress at the top of the pipe crown constant and had a negligible effect on the stress at the bottom of the crown.
Copyright (c) 2025 Soroosh Masoudnia, Pezhman Taghipour Birgani, Saeed Yaghoubi (Author) https://creativecommons.org/licenses/by/4.0
Vibration Analysis of a Sandwich Microbeam with Functionally Graded Porous Core and CNT Face Sheets, Considering Surface Effects
In this research, the vibration behavior of a sandwich microbeam with a graded porous core and carbon nanotube (CNT)-reinforced surfaces resting on a Visco-Pasternak foundation and taking surface effects into account is investigated. Moreover, to achieve accurate results, surface phenomena such as surface elasticity and residual stresses are incorporated by using the Mori-Tanaka homogenization method and Gurtin-Murdoch model, while the porous core's properties are characterized by a symmetric porosity distribution model. The governing equations are derived based on the third-order shear deformation theory (Reddy beam theory) and Hamilton’s principle. These equations are solved using the generalized differential quadrature method, accompanied by a detailed numerical study employing the modified couple stress theory (MCST). A parametric study is presented to investigate the impact of various characteristics, including the geometric properties porosity and distribution pattern of pores, mass fraction, type and distribution pattern of CNTs, length scale parameter, foundation parameters, and boundary conditions. Results reveal that increasing both the core porosity ratio and mass fraction of CNTs leads to an increase in the microbeam's natural frequencies and damping. The presented results can be used in the optimal design and analysis of the lightweight and robust structures in aerospace and advanced engineering applications.
Copyright (c) 2026 Arezo Havazadeh, Ali Ghorbanpour Arani, Hamed Khani Arani (Author) https://creativecommons.org/licenses/by/4.0
Stress Analysis for FGM Sphere in the Couple Stress Elasticity
This study develops an analytical framework based on Modified Couple Stress Theory (MCST) to investigate the stress response of functionally graded hollow spheres. The governing equations, which consider both material gradation and microstructural length-scale parameters, are solved with high accuracy using the Generalized Differential Quadrature (GDQ) method. The proposed framework exhibits numerical stability and strong convergence, and shows excellent agreement with benchmark analytical solutions reported in the literature, with a deviation of less than 3%. For a microstructural length-scale parameter of 0.1 μm, the results are in close agreement with classical elasticity predictions, with a deviation of less than 2%, confirming the robustness and reliability of the formulation in a multiscale context. Furthermore, increasing the material gradient index increases the sensitivity of the stress to the length-scale parameter, highlighting the coupling between material composition and microstructural effects. This integrated MCST-GDQ approach provides a solid and efficient foundation for further research on microstructured materials, smart composites, and multiscale mechanical systems.
Generalized Differential Quadrature (GDQ)
Copyright (c) 2026 Foad Saadi, Mohsen Jabbari, Mehdi Yarmohammad Tooski (Author) https://creativecommons.org/licenses/by/4.0
ANN simulation and thermo-flow optimization of a Non-Polar Hybrid CuO nanofluid
Nanoparticles (NPs) can improve the thermo-physical properties of the fluids and increase the effectiveness of heat transfer systems. In this way, finding the optimal properties of nanofluids (NFs) is very important. The present work aims to model and dynamic viscosity (DV) and thermal conductivity (TC) of CuO / 1-4 dioxane + Diethyl amine (DEA) as the non-polar NF with binary base fluids. The input parameters include the temperature and the solid volume fraction (SVF) of NPs. Based on available experimental data, the weight ratio of the NPs is 0.01 % to 0.06 % with temperatures ranging from 25oC to 45oC. The NF is modeled by the design and training of two separate two-layer feedforward artificial neural networks (ANNs) for the prediction of DV and TC at desired inputs of temperature and SVF. The average/maximum relative errors for test datasets are 0.3387/0.5078 and 0.3230/0.6871 for DV and TC prediction networks, respectively. Based on the designed model, a multi-objective optimization problem is defined to specify the maximum TC and minimum DV simultaneously and solved using the MOPSO method. Finally, the optimal values of the objective functions and the corresponding input parameters are plotted along with the Pareto optimal points.
Copyright (c) 2026 Mohammad Ali Fazilati, Ali Mokhtarian, Mojtaba Rahimi, Mohammad Hashemian (Author) https://creativecommons.org/licenses/by/4.0
Predicting One-Way slabs' Shear Capacity Subjected to Concentrated Loading Using ANN-Based Formulation
The main goal of this study is to present a neural network-based relationship to predict the shear capacity of one-way slabs under concentrated loads. For this purpose, after modeling 5 one-way slabs with different dimension ratios (between 2 and 3.33) by ETABS, the shear capacity of the slab for applying concentrated load along the long span (for eleven different positions) was calculated and the maximum deflection created in the slab was compared and controlled with the allowed value of the codes. After training the optimized neural network, using data obtained from ETABS, the shear capacity of slabs was predicted by MATLAB and the accuracy of this prediction was checked using the regression coefficient. Then, using data fitting and linear regression, the general equation for bearing capacity of the concrete slab in terms of the location of the concentrated load (α) was determined. Finally, in order to determine the accuracy of the presented equation, the real shear capacity of a one-way slab was calculated and compared with the numerical value obtained from the proposed equation. The obtained results indicate the acceptable accuracy of the proposed equation which could predict the shear capacity of the slabs by 96.39%.
Copyright (c) 2026 Ali Asghar Akbari Bargoshadi, Ashkan Khodabandehlou, Fedra Ashrafzadeh, Peyman Hamidi (Author) https://creativecommons.org/licenses/by/4.0
Effect of Non-ideal Boundary Conditions on Buckling of Rectangular Functionally Graded Plates
We have solved the governing equations for the buckling of rectangular functionally graded plates which one of its edges has small non-zero deflection and moment. For the case that the material properties obey a power law in the thickness direction, an analytical solution is obtained using the perturbation series. The applied in-plane load is assumed to be perpendicular to the edge which has non-ideal boundary conditions. Making use of the Linshtead-Poincare perturbation technique, the critical buckling loads are obtained. The results were then verified with the known data in the literature.
Copyright (c) 2024 Journal of Solid Mechanics
Effect of Stress Triaxiality on Yielding of Anisotropic Materials under Plane Stress Condition
The triaxiality of the stress state is known to greatly influence the amount of plastic strain which a material may undergo before ductile failure occurs. It is defined as the ratio of hydrostatic pressure, or mean stress, to the von Mises equivalent stress. This paper discusses the effects of stress triaxiality on yielding behavior of anisotropic materials. Hill-von Mises’s criteria for anisotropic material have been used with triaxiality factor (TF). Mathematical model that combines the yield stress and anisotropic ratio R (ratio of width strain to thickness strain) along with triaxiality have been formulated. This model is considered as an objective function subjected to inequality constraint. Constrained optimization is solved using genetic algorithm. The results obtained give the set of principal stresses along with corresponding critical triaxiality which is the maximum value at which the material can sustain without failure. If triaxiality extends further more the material will go to plastic deformation and may prone to failure. In this way, the critical triaxiality of materials can be determined to avoid fracture and failure of materials. This article is important from the industrial application point of view by considering triaxiality as a design parameter while designing the component.
Photoelastic Determination of Mixed Mode Stress Intensity Factors
A two dimensional finite model with inclined crack at different crack angles are being analyzed in mixed mode condition using photo elasticity method for the determination of Stress Intensity Factors. The well-known Sih’s equation and three points deterministic approach is used for the determination of stress intensity factors. The effects of biaxial load factor, crack angle, size factors were studied and a regression model was developed for geometry correction to predict Stress Intensity Factors. The results give a good compromise to the theoretical one. The experimental result also gives significant data for the two dimensional mixed mode loading conditions.
hp-Spectral Finite Element Analysis of Shear Deformable Beams and Plates
There are different finite element models in place for predicting the bending behavior of shear deformable beams and plates. Mostly, the literature abounds with traditional equi-spaced Langrange based low order finite element approximations using displacement formulations. However, the finite element models of Timoshenko beams and Mindlin plates with linear interpolation of all generalized displacements have suffered from shear locking, which has been alleviated with the help of primarily reduced/selective integration techniques to obtain acceptable solutions [1-4]. These kinds of 'fixes' have come into existence because the element stiffness matrix becomes excessively stiff with low-order interpolation functions. In this study we propose an alternative spectrally accurate hp/spectral method to model the Timoshenko beam theory and first order shear deformation theory of plates (FSDT) to eliminate shear and membrane locking. Beams and isotropic and orthotropic plates with clamped and simply supported boundary conditions are analyzed to illustrate the accuracy and robustness of the developed elements. Full integration scheme is employed for all cases. The results are found to be in excellent agreement with those published in literature.
Analysis of Wave Motion in a Micropolar Transversely Isotropic Medium
The present investigation deals with the propagation of waves in a micropolar transversely isotropic layer. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitudes of displacements and microrotation were also obtained. Finally, the numerical solution was carried out for aluminium epoxy material and the dispersion curves. Amplitudes of displacements and microrotation for symmetric and skew-symmetric wave modes are presented to evince the effect of anisotropy. Some particular cases are also deduced.
Temperature Effects on Nonlinear Vibration of FGM Plates Coupled with Piezoelectric Actuators
An analytical solution for a sandwich circular FGM plate coupled with piezoelectric layers under one-dimension heat conduction is presented in this paper. A nonlinear static problem is solved first to determine the initial stress state and pre-vibration deformations. By adding an incremental dynamic state to the pre-vibration state, the differential equations are derived. The role of thermal environment and control effects on nonlinear static deflections and natural frequencies imposed by the piezoelectric actuators using high input voltages are investigated. The good agreement between the results of this paper and those of the finite element (FE) analyses validated the presented approach. The emphasis is placed on investigating the effect of varying the applied actuator voltage and thermal environment as well as gradient index of FG plate on the dynamics and control characteristics of the structure.
Buckling Analysis of a Double-Walled Carbon Nanotube Embedded in an Elastic Medium Using the Energy Method
The axially compressed buckling of a double-walled carbon nanotabe surrounded by an elastic medium using the energy and the Rayleigh-Ritz methods is investigated in this paper. In this research, based on the elastic shell models at nano scale, the effects of the van der Waals forces between the inner and the outer tubes, the small scale and the surrounding elastic medium on the critical buckling load are considered. Normal stresses at the outer tube medium interface are also included in the current analysis. An expression is derived relating the external pressure to the buckling mode number, from which the critical pressure can be obtained. It is seen from the results that the critical pressure is dependent on the outer radius to thickness ratio, the material parameters of the surrounding elastic medium such as Young’s modulus and Poisson’s ratio. Moreover, it is shown that the critical pressure descend very quickly with increasing the half axial wave numbers.
Analysis on Centrifugal Load Effect in FG Hollow Sphere Subjected to Magnetic Field
This paper presents the effect of centrifugal load in functionally graded (FG) hollow sphere subjected to uniform magnetic field. Analytical solution for stresses and perturbation of the magnetic field vector are determined using the direct method and the power series method. The material stiffness, the magnetic permeability and the density vary continuously across the thickness direction according to the power law functions of radial directions. Magnetic field results in decreasing the radial displacement, the radial and shear stresses due to centrifugal load and has a negligible effect on circumferential displacement and also small effect compared with the other quantities on the circumferential stress due to centrifugal load. Increasing the angular velocity results in increasing the all above quantities due to magnetic field. With increasing the power law indices the radial displacement, the shear and circumferential stresses due to centrifugal load and magnetic field all are decreased and the radial stress due to centrifugal load and magnetic field increased.
A Rapidly Convergent Nonlinear Transfinite Element Procedure for Transient Thermoelastic Analysis of Temperature-Dependent Functionally Graded Cylinders
In the present paper, the nonlinear transfinite element procedure recently published by the author is improved by introducing an enhanced convergence criterion to significantly reduce the computational run-times. It is known that transformation techniques have been developed mainly for linear systems, only. Due to using a huge number of time steps, employing the conventional time integration methods requires quite huge computational time and leads to remarkable error accumulation, numerical instability, or numerical damping, especially for long investigation times. The present method specially may be extended to problems where the required time steps are of the order of the round-off errors (e.g., coupled thermoelasticty problems). The present procedure is employed for transient thermoelastic analysis of thick-walled functionally graded cylinders with temperature-dependent material properties, as an example. To reduce the effect of the artificial local heat and stress shock source generation at the mutual boundaries of the elements, second order elements are used. Influences of various parameters on the temperature and stress distributions are investigated. Furthermore, results of the proposed transfinite element technique are compared with the results obtained by other references to verify the validity, accuracy, and efficiency of the proposed method.
Effects of Geometric Nonlinearity on Stress Analysis in Large Amplitude Vibration of Moderately Thick Annular Functionally Graded Plate
This paper deals with the nonlinear free vibration of thick annular functionally graded material plates. The thickness is assumed to be constant. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The formulations are based on the first-order shear deformation plate theory and von Kármán-type equation. For harmonic vibrations, by using assumed-time-mode method sinusoidal oscillations are assumed, then the time variable is eliminated by applying Kantorovich averaging method. Thus, the basic governing equations for the problem are reduced to a set of ordinary differential equations in term of radius. The results reveal that vibration amplitude and volume fraction have significant effects on the resultant stresses in large amplitude vibration of the functionally graded thick plate.
Buckling Analysis of Simply-supported Functionally Graded Rectangular Plates under Non-uniform In-plane Compressive Loading
In this research, mechanical buckling of rectangular plates of functionally graded materials (FGMs) is considered. Equilibrium and stability equations of a FGM rectangular plate under uniform in-plane compression are derived. For isotropic materials, convergent buckling loads have been presented for non-uniformly compressed rectangular plates based on a rigorous superposition fourier solution for the in-plane Airy stress field and Galerkin’s approach for stability analysis. The results for isotropic case will be compared with reference articles and finite element method (FEM) solution. Finally, the results will be achieved for a sample of FGM material as well as the research on the effect of power law index on buckling coefficient.
Buckling Analysis of FG Plate with Smart Sensor/Actuator
In this paper, the active buckling control of smart functionally graded (FG) plates using piezoelectric sensor/actuator patches is studied. A simply supported FG rectangular plate which is bonded with piezoelectric rectangular patches on the top and/or the bottom surface(s) as actuators/sensors is considered. When a constant electric charge is imposed, the governing differential equations of motion are derived using the classical laminated plate theory (CLPT). The solution for the equation of motion is obtained using a Fourier series method and the effect of feedback gain on the critical buckling load for PZT-4 is studied .The buckling behavior of smart plate subjected to compressive load is also investigated. The sensor output is used to determine the input to the actuator using the feedback control algorithm. The forces induced by the piezoelectric actuators under the applied voltage field, enhance the critical buckling load
Wave Propagation in a Layer of Binary Mixture of Elastic Solids
This paper concentrates on the propagation of waves in a layer of binary mixture of elastic solids subjected to stress free boundaries. Secular equations for the layer corresponding to symmetric and antisymmetric wave modes are derived in completely separate terms. The amplitudes of displacement components and specific loss for both symmetric and antisymmetric modes are obtained. The effect of mixtures on phase velocity, attenuation coefficient, specific loss and amplitude ratios for symmetric and antisymmetric modes is depicted graphically. A particular case of interest is also deduced from the present investigation.
Simple Solutions for Buckling of Conical Shells Composed of Functionally Graded Materials
Using Donnell-type shell theory a simple and exact procedure is presented for linear buckling analysis of functionally graded conical shells under axial compressive loads and external pressure. The solution is in the form of a power series in terms of a particularly convenient coordinate system. By analyzing the buckling of a series of conical shells, under various boundary conditions and different material coefficients, the validity of the presented procedure is confirmed.
Effect of Through Stationary Edge and Center Cracks on Static Buckling Strength of Thin Plates under Uniform Axial Compression
Thin plate structures are more widely used in many engineering applications as one of the structural members. Generally, buckling strength of thin shell structures is the ultimate load carrying capacity of these structures. The presence of cracks in a thin shell structure can considerably affect its load carrying capacity. Hence, in this work, static buckling strength of a thin square plate with a centre or edge crack under axial compression has been studied using general purpose Finite Element Analysis software ANSYS. Sensitivity of static buckling load of a plate with a centre or a edge crack for crack length variation and its vertical and horizontal orientations have been investigated. Eigen buckling analysis is used to determine the static buckling strength of perfect and cracked thin plates. First, bifurcation buckling loads of a perfect thin plate with its mode shapes from FE eigen buckling analysis are compared with analytical solution for validating the FE models. From the analysis of the cracked thin plates, it is found that vertical cracks are more dominant than horizontal cracks in reducing buckling strength of the thin plates. Further, it is also found that as the crack length increases, buckling strength decreases.
Dynamic Stability of Functionally Graded Beams with Piezoelectric Layers Located on a Continuous Elastic Foundation
This paper studies dynamic stability of functionally graded beams with piezoelectric layers subjected to periodic axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The Young’s modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton’s principle, the governing dynamic equation is established. The effects of the constituent volume fractions, the influences of applied voltage, foundation coefficient and piezoelectric thickness on the unstable regions are presented.
Geometrical Optimization of the Cast Iron Bullion Moulds Based on Fracture Mechanics
In this paper, the causes of the crack initiation in cast iron bullion moulds in Meybod Steel Corporation are investigated and then some new geometrical models are presented to replace the current moulds. Finally, among the new presented models and according to the life assessment, the best model is selected and suggested as the replaced one. For this purpose, the three recommended moulds were modeled and analyzed by ANSYS software. First, a thermal analysis and then a thermo-mechanical coupled field analysis were performed on each three model. The results of the analysis are used to determine the critical zone. The critical zone is selected on the symmetric axis of the inner surface of the mould. By comparing the principle stress contours and temperature distribution contours of three models, one of the suggested models was selected as optimized geometrical model. Then, the crack modeling and the life assessment on the optimized model were implemented and the total life of the model was calculated. Comparison of the life of the optimized and the initial models shows an increase in the life of the suggested model. The results are verified with the experiments.
Buckling Analyses of Rectangular Plates Composed of Functionally Graded Materials by the New Version of DQ Method Subjected to Non-Uniform Distributed In-Plane Loading
In this paper, the new version of differential quadrature method (DQM), for calculation of the buckling coefficient of rectangular plates is considered. At first the differential equations governing plates have been calculated. Later based on the new version of differential quadrature method, the existing derivatives in equation are converted to the amounts of function in the grid points inside the region. Having done that, the equation will be converted to an eigen value problem and the buckling coefficient is obtained. Solving this problem requires two kinds of loading: (1) unaxial half-cosine distributed compressive load and (2) uni-axial linearly varied compressive load. Having considered the answering in this case and the analysis of the effect of number of grid points on the solution of the problem, the accuracy of answering is considered, and also the effect of power law index over the buckling coefficient is investigated. Finally, if the case is an isotropic type, the results will be compared with the existing literature.
Mechanical Behavior of an Electrostatically-Actuated Microbeam under Mechanical Shock
In this paper static and dynamic responses of a fixed-fixed microbeam to electrostatic force and mechanical shock for different cases have been studied. The governing equations whose solution holds the answer to all our questions about the mechanical behavior is the nonlinear elasto-electrostatic equations. Due to the nonlinearity and complexity of the derived equations analytical solution are not generally available; therefore, the obtained differential equations have been solved by using of a step by step linearization method (SSLM) and a Galerkin based reduced order model. The pull-in voltage of the structure and the effect of shock forces on the mechanical behavior of undeflected and electrostatically deflected microbeam have been investigated. The proposed models capture the other design parameters such as intrinsic residual stress from fabrication processes and the nonlinear stiffening or stretching stress due to beam deflection.
Transverse Vibration of Clamped and Simply Supported Circular Plates with an Eccentric Circular Perforation and Attached Concentrated Mass
In this investigation Rayleigh-Ritz variational method has been applied to determine the least natural frequency coefficient for the title problem. Classical plate theory assumptions have been used to calculate strain energy and kinetic energy. Coordinate functions are combination of polynomials which satisfy boundary conditions at the outer boundary and trigonometric terms. In the second part of this study ABAQUS software is used to compute vibration natural frequency for some special combinations of geometrical and mechanical parameters. Then results of Rayleigh-Ritz method have been obtained for the mentioned special cases. It can be seen that the agreement between them is acceptable.
Free Vibration of Functionally Graded Beams with Piezoelectric Layers Subjected to Axial Load
This paper studies free vibration of simply supported functionally graded beams with piezoelectric layers subjected to axial compressive loads. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton’s principle, the governing equation is established. Resulting equation is solved using the Euler’s Equation. The effects of the constituent volume fractions, the influences of applied voltage and axial compressive loads on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.