Semianalytical methods for analyzing stress concentrations in thick-walled multilayered composites

For analyzing the stress, strain, and displacement fields in thick-walled anisotropic multilayered composites, sophisticated semianalytical solution methods based on a first-order shear deformation theory have been developed at the Insitut für Leichtbau und Kunststofftechnik and validated in a great number of numerical finite-element simulations and extensive experimental tests. A comparison of results obtained by the different methods for general multilayered composites made from unidirectional, bidirectional, and textile-reinforced layers show a good agreement.     

Compressive stability of multilayered delaminations in composites

The behavior of defects of the near-surface crack type was investigated in laminated composites. Multilayered delaminations in compressed elements were examined on the assumption that cylindrical bending of the delamination is accompanied by shear within the framework of a model similar to the Timoshenko model. The effect of the mechanical properties and thickness and number of layers in the delaminated section on the critical buckling strain and strain corresponding to the beginning of growth of the delamination was investigated. It was shown that when the delaminated section contains several bearing layers and the rigidity of the composite with respect to interlaminar shear is small, consideration of the shear in the delaminated section can lead to a significant change in the critical compressive strains and/or critical size of the delamination.Translated from Mekhanika Kompozitnykh Materialov. Vol. 33, No. 3, pp. 312–320, May–June, 1997.     

Special finite elements including stress concentration effects of a hole

Special finite elements are developed for efficient evaluation of stress concentration around a hole in complex structures. The complex variable formulation is used to derive a special set of stress functions which embody the stress concentration effects of a hole. The stress functions in combination with an independent displacement field assumed along the element boundary are used to construct the special elements with the hybrid displacement finite element method. Several numerical examples are presented to show that the used of special finite elements to model critical regions around a hole, together with conventional finite elements to model other regions away from the hole, is not only very convenient but also highly accurate.     

Analytical and experimental evaluation of stresses in elastic annuli subjected to three-point loading on the outer surface

An analytical solution based on the implementation of the Fourier series is presented for the full-field analysis of stresses in an annular plate subjected to external force loadings uniformly distributed over three small segments of the outer periphery when two of those segments are symmetrical about the diameter passing through the center of the third segment. This problem refers to an annular plate which rests upon two equidistant platens when compressed by a vertical locally-distributed force. The obtained theoretical results are compared with a series of photoelastic experiments for different distances between the loaded segments of the rim.  The feasibility of the mathematical model for the mixed-type boundary conditions is analyzed by comparison of the experimental results, the theoretical analysis, and FEM numerical simulation.     

Singular stress analysis near sharp corners in anisotropic notched plates subjected to bending loads

This paper presents an analytical approach to determine the singular stress fields near sharp corners in anisotropic notched plate subjected to bending. The first-order shear deformation plate theory (FSDPT) is used and the material anisotropy is modeled by the Stroh formalism. Based on the Mellin transform method, the stress singularity orders as well as the stress intensities are determined analytically. The results presented in this paper give us the singular behaviors for various plate angle α, material orientation angles ϕ and the anisotropic parameters ε. These new findings are helpful in reducing or even eliminating the singularities near the sharp corner.     

Analytical modelling for static stress analysis of pin-loaded lugs with bush fitting

Pin-loaded connections are widely used in the industry. Connecting rods of reciprocating engines in automotive applications or pin-loaded lugs of landing gears and airframe structures can be cited as examples. These systems are subject to thermomechanical cyclic loadings and fatigue mechanisms are often observed. The calculation of stresses in the lug is crucial in view of a fatigue lifetime analysis. Analytical modelling may be very helpful in the early design stage, by allowing fast parametric studies and the identification of the most influent parameters on the response in stresses. In this paper, we propose analytical models for bush fitting and pin-loading conditions, leading to the complete calculation of the stress distribution in the lug. In each case, the analytical solutions are compared with finite element simulations. In the last part, we perform a sensitivity analysis as an application of the presented analytical tools.     

A non-conforming finite element for limit analysis of periodic composites

In this work, a non-conforming three-dimensional finite element coupled with direct methods and homogenization technique is presented for the limit analysis of periodic metal-matrix composites. Using this element, which is constructed from bilinear shape functions and enriched by internal second-order polynomials, limit analysis of composite material can be efficiently carried out. Accuracy and overall performance are illustrated through comparison with different structural solid elements in the context of direct as well as incremental methods. It is shown that the limit domain of periodic composites for different fiber distributions and volume fractions provides a foundation for the structural design. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calculation of the moisture concentration field in a multilayered plate

Conclusion Thus, we have developed an algorithm and program to calculate fields of moisture concentration in a laminated plate for steady external temperatures and moisture contents. A test calculation and comparison of some of the findings with previous results demonstrated the accuracy of the program for solving a number of diffusion problems. For example, the program can be used to evaluate the life of the moisture-protective properties of polymer products, as well as to model moisture absorption in fiber composites.Curves of moisture concentration were calculated for a unidirectionally reinforced (with organic fibers) plastic at different relative humidities. We also calculated sorption curves and isotherms, which were shown to agree satisfactorily with previous empirical curves. It was shown that it is possible to approximately evaluate the sorption behavior of a unidirectionally reinforced fiber composite by means of a three-layer model and to analyze the stability of the result against an increase in the number of layers. For the two-component composite examined here, sorption behavior deviates from the classical behavior described by Fick's law — although the components of the composite obey this law.The algorithm and program that were developed make it possible to evaluate the kinetics of moisture absorption in complex composite systems and determine the distribution of moisture among and within the components.The study described here was conducted under grant 93.176 from the Latvian Science Council.Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 4, pp. 502–511, July–August, 1994.     

Holonomy groups of Bieberbach groups with finite outer automorphism groups

This work was supported by the DFG and by a Polish grant BW/5100-5-0116-3.     

Plane stress finite element analysis of filler reinforced polymers

The characteristics of polymers such as force-deformation behaviour, strength, fatigue and wear resistance, can be tailored by embedding it with filler particles. The influence of the fillers on the material behaviour significantly depends on the size and geometric form of the filler aggregates, which vary under mechanical loading. The concept of super element is used to model filler particles. This is now coupled with the polymer matrix to generate a finite element model of filler reinforced polymers. In this work, we investigate the effect of filler geometry and volume fraction of fillers on the overall stiffness of the filler reinforced polymer. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A finite element method for interface problems in domains with smooth boundaries and interfaces

This paper is concerned with the analysis of a finite element method for nonhomogeneous second order elliptic interface problems on smooth domains. The method consists in approximating the domains by polygonal domains, transferring the boundary data in a natural way, and then applying a finite element method to the perturbed problem on the approximate polygonal domains. It is shown that the error in the finite element approximation is of optimal order for linear elements on a quasiuniform triangulation. As such the method is robust in the regularity of the data in the original problem.     

A priori bounds in the Bénard problem with boundaries of finite conductivity

In questa nota, si danno alcune stime a priori per le soluzioni classiche delle equazioni che descrivono il problema di Bénard quando le frontiere hanno conduttività finita (modello di Hurle, Jakeman e Pike [3]). Adottando il metodo della funzione peso, si mostra che la velocità v e la temperatura T del fluido che a priori sono fatte crescere per grandi distanze spaziali, si mantengono in effetti uniformemente limitate a patto che siano tali la velocità e la temperatura iniziali del fluido e il suo gradiente di pressione.     

A combined finite/discrete element algorithm for delamination analysis of composites

A combined finite/discrete element method is developed to model delamination behaviour in laminated composites. A penalty based algorithm is employed to evaluate the interlaminar stress state. The failure surface for delamination is defined by a Chang-Springer criterion, and the interlaminar crack propagation is achieved by a standard discrete element contact/release algorithm. The ability of the method for simulation of this behaviour is assessed by solving standard test cases available from the literature.     

RMVT- and PVD-based finite cylindrical layer methods for the three-dimensional buckling analysis of multilayered FGM cylinders under axial compression

The unified formulations of finite cylindrical layer methods (FCLMs) based on the Reissner mixed variational theorem (RMVT) and the principle of virtual displacements (PVD) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, multilayered functionally graded material (FGM) circular hollow cylinders and laminated composite ones under axial compression. The material properties of the FGM layer are assumed to obey the power-law distributions of the volume fraction of the constituents through the thickness coordinate. In these formulations, the cylinder is divided into a number of finite cylindrical layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-surface variations of the primary variables of each individual layer, respectively, as well as the related order of each primary variable can be freely chosen, such as the layerwise linear, quadratic or cubic function distribution through the thickness coordinate. The accuracy and convergence of the RMVT- and PVD-based FCLMs developed in this article are assessed by comparing their solutions with the exact 3D solutions available in the literature.     

Scaled boundary finite element analysis of stress singularities in piezoelectric multi-material systems

The scaled boundary finite element method (SBFEM) in an extension for piezoelectric materials is used to analyze twoand three-dimensional stress singularities in piezoelectric multi-material systems. It is found to be an efficient tool for the analysis of singularity orders of such situations, that turn out to be rather complex. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)