2202 複合材料楕円板の座屈と振動に関する積層構成最適化(OS15 異方性構造の力学と設計I)

Shape optimization in laminated composite plates

This work presents an analytical approach and accurate numerical results for the free vibration of symmetrically laminated, thick composite circular and elliptical plates. The shear deformation through the thickness is considered by employing the first-order shear deformation theory. The problem is solved by the Ritz method and the natural frequencies are calculated for three-layered, simply supported and clamped plates with stacking sequence [θ/−θ/θ]. Particularly, extensive results are presented by using various shear correction factors for a wide range of geometric parameters, and the effects of varying the factor upon the free vibration frequencies of the laminated circular and elliptical plates are discussed.

Optimal elastic buckling loads of spatially heterogeneous plates formed from a series of composite patches is considered. Reissner-Mindlin laminated composite plate theory including thermal effects is adopted for the analysis and the problem is solved using the finite element method based on a bi-cubic Lagrange C° element formulation. The thermal residual stresses considered are those that result during elevated temperature processing because of the different laminates forming the patches of the plate. In the optimization, the fiber angles in each patch are the design variables and three symmetric laminated plate configurations are investigated. The results illustrate that thermal residual effects can lead to optimal buckling loads which are as much as two times greater than the corresponding optimal buckling loads in which these manufacturing effects are ignored. The work demonstrates the importance of spatial heterogeneity as well as the significance ofmanufacturing-induced residual stresses in optimal design studies of composite structures.

Compared with traditional metal-materials, fiber-reinforced composite materials have better performance in many aspects such as strength, stiffness, and fracture resistance. At present, fiber-reinforced composite materials have been widely used in automotive, aerospace, and other industrial fields. This paper proposes a topology optimization method for solving the fundamental frequency maximization of undamped free vibration of continuous fiber-reinforced composite structures. To achieve the simultaneous optimization of the structural topological configuration and the fiber angle. A dynamic topological optimization model is established with the permitted material usage as the constraint and the structure's first-order eigenvalue as the objective function. The model includes density design variables that characterizes the topological configuration of the structure and angular design variables that characterizes the fiber orientation. The analytical sensitivity formulas of the objective function of eigenvalue with respect to density design variables and angle design variables are derived in detail, and the method of moving asymptotes (MMA) is used to solve the optimization problem. Finally, three numerical examples are performed to verify the effectiveness of the proposed method, which includes a static optimization example with the stiffness maximization as the goal and two dynamic optimization examples with the first-order eigenvalue maximization as the goal. The results show that the proposed method can achieve a stable iterative history and fast convergence, and can effectively improve the structural frequency while achieving the integrated optimization of the structural topological configuration and the fiber angle.

Optimization of composite I-sections using fiber angles as design variables

Buckling of laminated composite and sandwich beams due to axially varying in-plane loads

Stress intensity factors numerically investigated the Mode I loading of composite plates with an edge crack and repaired with a patch on a single side. The effect of the fiber orientation angle for both composite plate and the patch were analyzed with regard to crack length, adhesive properties, and plate thickness. The stress intensity factors were calculated by using the quarter point element that can be applied to 3D crack problems of homogeneous anisotropic materials.It was observed in this study that the fiber orientation angle affects the stress intensity factors significantly.

On the basis of the three-dimensional theory of elasticity, a graded finite element method capable of modeling static and dynamic behaviors of elliptical plates made of functionally graded materials (FGMs) subjected to uniform pressure is developed. In the present paper, two different material properties distributions are considered. For the dynamic analysis, the effective through-the-thickness continuous material properties distribution of the FGM (which is assumed to be composed of ceramic and metallic constituents) is determined based on Mori–Tanaka homogenization technique. The three-dimensional graded finite element formulation is derived based on the principle of minimum potential energy and Rayleigh Ritz method. To solve the time-dependent equations, Newmark’s direct integration method is employed. To present the efficiency of the present work, several numerical examples are included. Since similar results are not available in the literature, results of the present formulations are verified by comparing them with available ones of a homogenous elliptical plate.

This paper deals with frequency optimization of symmetrically laminated angle-ply annular sector plates. The design objective is the maximization of the fundamental frequency and the design variable is the fiber orientation in the layers. The first order shear deformation theory is used for the finite element solution of laminates. Nine-node Lagrangian rectangular plate element which have five degrees of freedom per node is used for the finite element solution of the laminated annular sector plates. The modified feasible direction method is used for the optimization routine. For this purpose, a program based on FORTRAN is used. The numerical analysis is carried out to investigate the effects of annularity, boundary conditions and sector angle on the optimal designs and the results are shown in tabular and graphical forms. Finally, the obtained results are compared. It can be shown that the parameters have a key role on the optimum design of laminated annular sector plates.

GASWAT-PC is a microcomputer material balance program that calculates original gas in place (OGIP) from production history for gas reservoirs with or without water influx. Several well-known analytical techniques, and some extensions and improvements, are applied to a single input data set. The output for each method is given in both tabular and graphical form. GASWAT-PC also has the capability to predict reservoir pressure and recovery efficiency for a specified production rate if OGIP and aquifer properties are known. An option is included to account for the effect of a large pressure gradient in the water-invaded region. Case studies illustrate the application of GASWAT-PC to an abnormally pressured reservoir and to two water drive reservoirs. Finally, we compare the pressure performance predicted by a numerical simulator and by GASWAT-PC for a water drive reservoir with a high dip.

Audiometers—A Closer Look

Inelastic response of elliptical plates to impact and initial impulsive loading is studied.For determination of the deflected shape of plates the concept of mode form motions amalgamated with the conical velocity field in used.Theoretical predictions of residual deflections are developed for plates of piece wise constant thickness.The cases of circular and annular plates subjected to initial impulsive loading are studied as particular cases of an elliptical plate.

Fundamental frequencies of solid and annular elliptical plates were approximated using the static deflections by means of finite element method (FEM) without computing the eigenvalues. The problem was formulated within the framework of the first order shear deformation theory (FSDT). The effects of (i) the inner and outer boundary conditions, (ii) the size of the perforation, (iii) the aspect ratio, and (iv) the thickness of the plate on the performance of the method were examined via a large variety of numerical simulations. Convergence study was performed through h-refinement. Accuracy of the results was validated through comparison studies. The results reveal that the application of the Morley’s formula which does not require eigenvalue analysis approximates the fundamental frequency with finer mesh compared to the eigenvalue analysis. The method can be considered as a practical technique to approximate the fundamental frequency. However, the boundary conditions have dominant role on the accuracy of the solution particularly when the plate is perforated.

The aim of this paper is to compare the static deflections and stress results of layered and functionally graded composite beams under static load. In the comparison study, the results obtained for a cantilever beam under point load. The Timoshenko beam and the Euler-Bernoulli beam theories are used in the beam model. The energy based Ritz method is used for the solution of the problem and algebraic polynomials are used with the trivial functions for the Ritz method. Two different materials are considered as layered and functionally graded distribution in a cantilever beam and their static deflections, stress distributions are compared under a point load at free end of the beam. For two different distributions, the formulations of Ritz method are obtained and solved numerically. In the numerical results, the effects of material distribution parameter, aspect ratio on the static deflections and stress distribution of functionally graded beams are obtained and compared with the results of the layered composite beam. Difference among of beam theories are compared for functionally graded and layered beams. Also, some comparison studies are performed in order to validate the using formulations.

Sound radiation and transmission loss characteristics of variable stiffness composite plate reinforced with the curvilinear fibers are investigated numerically. The formulation is developed using higher-order shear flexible finite element model combined with Helmholtz wave equation. The governing equations obtained using Hamilton’s approach are further solved through the modal super position method to analyze the vibration response under steady state excitation. The inherent material damping of the laminate is accounted through the modal damping calculated using the modal strain energy approach. The acoustic pressure of the variable stiffness laminates is estimated using the Raleigh integral. Subsequently, acoustic response characteristics such as acoustic power level, radiation efficiency, directivity pattern, and transmission loss from the laminates are predicted using the estimated sound pressure for various forcing frequencies. A parametric study covering a wide range of design variables including center and edge fiber angles, lamination scheme, thickness ratio, and boundary conditions on the acoustic sound behavior arising from the vibration of curvilinear fiber composite plate is detailed. This study reveals that the acoustic response of the curvilinear fiber composite plate is significantly influenced by the curvilinear fiber angles at the center/edge fiber angle of the layers. It is hoped that the results obtained here will be useful for designers in developing structures with desired acoustic response characteristics.