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Geometrically nonlinear and elastoplastic behavior of a circular FGM (functionally graded material) plate under mechanical loading–unloading condition is investigated employing three-dimensional finite element method (FEM) modeling. The through-thickness material distribution of the FGM plate is defined by a power-law variation. The elastic mechanical properties and the elastoplastic material behavior of the FGM plate described respectively by the Mori–Tanaka scheme and the TTO (Tamura–Tomota–Ozawa) model are implemented in the FEM model. The FEM model is validated presenting a very good agreement with the studies from the literature. The influences of nonlinearity, especially the elastoplastic and elastoplastic with geometrically nonlinear behavior, load parameter and thickness-to-radius ratio in terms of nonlinearity, and material composition on the mechanical behavior of the FGM plate are examined. The FEM results are evaluated in terms of the permanent central deflection and the plastic equivalent stress distributions of the FGM plate. The results indicate that a considerable difference occurs between the elastoplastic and elastoplastic with geometrically nonlinear behavior of the FGM plate in terms of both the permanent central deflection and the plastic equivalent stress distributions except ceramic-rich composition that has almost a linear–elastic material behavior, and the geometrical nonlinearity becomes an important parameter with increasing load parameter and decreasing thickness-to-radius ratio. The combination of geometrical and material nonlinearities exhibits a significant influence on the nonlinear mechanical behavior of the FGM plate under plastic deformation. [ABSTRACT FROM AUTHOR]

Macroscopic modeling of architected materials requires the identification of local modes of deformation in addition to the usual global degrees of freedom—usually based on intuitive understanding. Most of the recent work in this field have used couple stress or micropolar theories with the intention to account for local rotational degrees of freedom. This work presents a systematic, principal component analysis-based technique for identifying these local modes of deformation and degrees of freedom of deformation of architected structures from full-scale FEA or experimental data. We demonstrate that using such an approach, we can identify the principal modes of deformation of a web core beam, and that in addition to "microrotation," we need to include two additional degrees of freedom which we roughly refer to as "microbowing mode" and "microspline mode." We then develop an energy minimization (Ritz method)-based approach to directly obtain the discrete equations of equilibrium with five local degrees of freedom at each material point of the beam (the macrodeflection, macrorotation, microrotation, microbow and microspline), thereby obviating the need to postulate balance laws for micromorphic continua a priori. We use this combined strategy and validate the resulting model by simulating the response of web core beams and compare with full-scale FEA simulations. The results illustrate the efficacy of the method in modeling the complex deformation modes of the web-core beam with very few elements and is able to predict the regions where wrinkling of the beam face plates are most pronounced. This SVD+energy approach can be completely generalized to identify the necessary additional internal degrees of freedom and equilibrium equations for other types of architected structures either from detailed FEA simulations or experimental data. [ABSTRACT FROM AUTHOR]

This is a review paper containing the governing equations and analytical solutions of the classical and shear deformation theories of functionally graded straight beams. The classical, first-order, and third-order shear deformation theories account for through-thickness variation of two-constituent functionally graded material, modified couple stress (i.e., strain gradient), and the von Kármán nonlinearity. Analytical solutions for bending of the linear theories, some of which are not readily available in the literature, are included to show the influence of the material variation, boundary conditions, and loads. [ABSTRACT FROM AUTHOR]

For thermoelastic solids, rate of mechanical work equilibrates with the rate of kinetic energy and rate of strain energy. In this article, this aspect of the physics is utilized to: (i) derive an alternate form of the energy equation based on the first law of thermodynamics and (ii) derive an alternate form of entropy inequality based on the second law of thermodynamics, both free of rate of strain energy. This alternate form of entropy inequality strictly contains physics related to the rates of entropy. This form of entropy inequality is essential to show that the constitutive theories for stress tensor for thermoelastic solids are free of any thermodynamic restrictions and thus can be derived independently of the entropy inequality. In this article, we explore both forms of entropy inequality, one containing rate of strain energy and the alternate form that is free of rate of strain energy in deriving the constitutive theories for the stress tensor. It is shown that the alternate for entropy inequality free of rate of strain energy provides greater flexibility in deriving the constitutive theories for the stress tensor as it places no thermodynamic restrictions on the constitutive theories for the stress tensor. Both forms of the entropy inequality are examined for establishing dependent variables and their arguments for deriving constitutive theories for such solids in Lagrangian description. The solid matter is assumed to be homogeneous, isotropic, compressible, aswell as incompressible, but the deformation and the strains can be finite. [ABSTRACT FROM AUTHOR]

A weak form Galerkin finite element model for the nonlinear quasi-static and fully transient analysis of initially straight viscoelastic beams is developed using the kinematic assumptions of the third-order Reddy beam theory. The formulation assumes linear viscoelastic material properties and is applicable to problems involving small strains and moderate rotations. The viscoelastic constitutive equations are efficiently discretized using the trapezoidal rule in conjunction with a two-point recurrence formula. Locking is avoided through the use of standard low-order reduced integration elements as well through the employment of a family of elements constructed using high-polynomial order Lagrange and Hermite interpolation functions. [ABSTRACT FROM AUTHOR]

A nonlocal Timoshenko curved beam model is developed using a modified couple stress theory and Hamilton's principle. The model contains a material length scale parameter that can capture the size effect, unlike the classical Timoshenko beam theory. Both bending and axial deformations are considered, and the Poisson effect is incorporated in the model. The newly developed nonlocal model recovers the classical model when the material length scale parameter and Poisson's ratio are both taken to be zero and the straight beam model when the radius of curvature is set to infinity. In addition, the nonlocal Bernoulli-Euler curved beam model can be realized when the normal cross-section assumption is restated. To illustrate the new model, the static bending and free vibration problems of a simply supported curved beam are solved by directly applying the formulas derived. The numerical results for the static bending problem reveal that both the deflection and rotation of the simply supported beam predicted by the new model are smaller than those predicted by the classical Timoshenko curved beam model. Also, the differences in both the deflection and rotation predicted by the current and classical Timoshenko model are very large when the beam thickness is small, but they diminish with the increase of the beam height. Similar trends are observed for the free vibration problem, where it is shown that the natural frequency predicted by the nonlocal model is higher than that by the classical model, and the difference between them is significantly large only for very thin beams. These predicted trends of the size effect at the micron scale agree with those observed experimentally. [ABSTRACT FROM AUTHOR]

Thermal residual stresses, internal pressure stresses, and acceleration stresses during launch were evaluated and quantified for cryogenic composite fuel tank design. Both failure initiation and progression of graphite/epoxy laminate system (IM7/977-2) [0/90/90/0/0/90]s and graphite/BMI laminate system (IM7/5250-4) [0/90/90/0/0/90]s were investigated using the non-isothermal classical laminate and plate theory (CLPT) and the maximum stress failure criterion. The thermal residual stresses in the transverse direction are the dominant stresses on each ply in the launch stage. After initial ply cracking, through-the-thickness temperature change of a laminate related to fuel leakage as well as a laminate stiffness matrix change was applied to the progressive failure analysis. The fuel leakage-based progressive analysis shows a higher number of initial ply cracking does not necessarily mean a higher chance of matrix cracking in all plies. The graphite/BMI laminate has such an advantage as transverse thermo-mechanical resistance over the graphite/epoxy laminate at an initial exposure to -253°C and 1500 kPa. In terms of complete laminate matrix cracking, however, the graphite/epoxy laminate is more resistant to transferring stresses to other plies than the graphite/BMI laminate. [ABSTRACT FROM AUTHOR]

Geometrically nonlinear analysis of functionally graded circular plates subjected to mechanical and thermal loads is carried out in this paper. The Green–Lagrange strain tensor in its entirety is used in the analysis. The locally effective material properties are evaluated using homogenization method which is based on the Mori–Tanaka scheme. In the case of thermally loaded plates, the temperature variation through the thickness is determined by solving a steady-state heat transfer (i.e. energy) equation. As an example, a functionally gradient material circular plate composed of zirconium and aluminum is used and results are presented in graphical form. [ABSTRACT FROM AUTHOR]

A consistent third-order shell theory with applications to composite circular cylinders is presented and its finite element formulation is developed. The formulation has seven displacement functions and requires CO continuity in the displacement field. The exact computation of stress resultants is carried out through numerical integration of material stiffness coefficients of the laminate. A displacement finite element model is developed using Lagrange elements with higher-order interpolation polynomials. These elements preclude any effect of shear and membranes locking. Comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and composite cylindrical shells are found to be excellent and show the validity of the developed shell theory and its implementation into a finite element code. [ABSTRACT FROM AUTHOR]

Linear and nonlinear thermomechanical response of the functionally graded (metal-ceramic) plates subjected to static and dynamic loads is studied. The third-order plate theory of Reddy with the von Kármán geometric nonlinearity is used for the kinematic and kinetic descriptions, and two constitutent power-law distribution through the plate thickness is employed. A displacement finite element model is developed with the Newmark time integration scheme, and the Newton-Raphson iterative procedure is used for the solution of nonlinear algebraic equations. While the model is general enough to be used for any boundary conditions, the simply supported and clamped boundary conditions are used to study the parametric effect of the power-law index and surface temperatures and mechanical loads on the thermomechanical response. The most significant finding of this study is that the deflection response does not fall intermediate to those of the metal or ceramic plates. This is due to the nonlinear coupling of mechanical and thermal contributions. [ABSTRACT FROM AUTHOR]

Presents a computational procedure for accurate determination of interlaminar stresses in thick and thin composite laminates subjected to torsional loading. Description of a multilevel hierarchical basis preconditioner; Analysis of the torsion problem; Torsion of a cantilevered laminate.

In this paper a unified finite element model that contains the Euler–Bernoulli, Timoshenko and simplified Reddy third-order beam theories as special cases is presented. The element has only four degrees of freedom, namely deflection and rotation at each of its two nodes. Depending on the choice of the element type, the general stiffness matrix can be specialized to any of the three theories by merely assigning proper values to parameters introduced in the development. The element does not experience shear locking, and gives exact generalized nodal displacements for Euler–Bernoulli and Timoshenko beam theories when the beam is homogeneous and has constant geometric properties. While the Timoshenko beam theory requires a shear correction factor, the third-order beam theory does not require specification of a shear correction factor. An extension of the work to axisymmetric bending of circular plates is also presented. A stiffness matrix based on the exact analytical form of the solution of the first-order theory of circular plates is derived. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the present study a hybrid boundary-element and finite-element method is developed for the non-linear analysis of two-dimensional elastic media with inclusions, and it is utilized in defining the micro- mechanical stress field in composite materials. The linear elastic, isotropic and homogeneous matrix is treated with the BEM, while the non-linear elastic and orthotropic inclusions (fibres) are treated with the FEM. [ABSTRACT FROM AUTHOR]

A general two-dimensional shear deformation theory of laminated composite plates is presented. The theory accounts for a desired degree of approximation of the displacements through the laminate thickness. As special cases, the classical, first-order (Reissner-Mindlin) and other shear deformation theories available in the literature can be deduced From the present theory. [ABSTRACT FROM AUTHOR]

Focuses on the importance of plane stress solution to accurately predict the ion-beam projection lithographic masks deformations in order to enhance the quality of the microcircuit to be manufactured. Use of an alternative displacement approach in rectangular coordinates; Plane stress constitutive relation for an isotropic material yields, including the Poisson ratio; Overview of the buckling modal shape for a clamped vertical circular plate subjected to gravity.

A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures that have one geometric dimension much smaller than the other two. A new notion of curved bonds is exploited to cater for force transfer between the peridynamic particles describing the shell. Starting with the three dimensional force and deformation states, appropriate surface based force, moment and several deformation states are arrived at. Upon application on the curved bonds, such states yield the necessary force and deformation vectors governing the motion of the shell. By incorporating a shear correction factor, the formulation also accommodates analysis of shells that have higher thickness. In order to attain this, a consistent second order approximation to the complementary energy density is considered and incorporated in peridynamics via constitutive correspondence. Unlike the uncoupled constitution for thin shells, a consequence of a first order approximation, constitutive relations for thick shells are fully coupled in that surface wryness influences the in-plane stress resultants and surface strain the moments. Our proposal on the peridynamic shell theory is numerically assessed against simulations on static deformation of spherical and cylindrical shells, that of flat plates and quasi-static fracture propagation in a cylindrical shell. [ABSTRACT FROM AUTHOR]

In conventional analyses of composite laminates, the assumption of perfect bonding of adjoining layers is well accepted, although this is an oversimplification of the reality. It is possible that the bond strength may be less than that of the laminae. Thus, the study of weak bonding is an interesting focus area. In this study, an elastic bonding model based on three-dimensional theory of elasticity in a layerwise framework is used to study composite laminates. The differential quadrature (DQ) discretization is used to analyze the layerwise model. The present model enables the simulation of actual bonding stress states in laminated structures. The interfacial characteristics of transverse stress continuity as well as the kinematic continuity conditions are satisfied through the inclusion of the elastic bonding layer. The present model is employed to investigate the free vibration of thick rectangular cross-ply laminates of different boundary conditions and lamination schemes. [ABSTRACT FROM AUTHOR]