A finite element model based on the layerwise theory is developed for the analysis of transverse cracking in cross-ply laminated beams. The numerical model is developed using the layerwise theory of Reddy, and the von Kármán type nonlinear strain field is adopted to accommodate the moderately large rotations of the beam. The finite element beam model is verified by comparing the present numerical solutions with the elasticity solutions available in the literature; an excellent agreement is found. The layerwise beam model is then used to investigate the influence of transverse cracks on material properties and the response in cross-ply laminates using a multiscale approach. The multiscale analysis consists of numerical simulations at two different length scales. In the first scale, a mesoscale, a systematic procedure to quantify the stiffness reduction in the cracked ply is proposed exploiting the laminate theory. In the second scale, a macroscale, continuum damage mechanics approach is used to compute homogenized material properties for a unit cell, and the effective material properties of the cracked ply are extracted by the laminate theory. In the macroscale analysis, a beam structure under a bending load is simulated using the homogenized material properties in the layerwise finite element beam model. The stress redistribution in the beam according to the multiplication of transverse cracks is taken into account and a prediction of sequential matrix cracking is presented. تفاصيل المقالة

In this paper, a comparison of weak-form Galerkin and least-squares finite element models of Timoshenko beam theory with the von Kármán strains is presented. Computational characteristics of the two models and the influence of the polynomial orders used on the relative accuracies of the two models are discussed. The degree of approximation functions used varied from linear to the 5th order. In the linear analysis, numerical results of beam bending under different types of boundary conditions are presented along with exact solutions to investigate the degree of shear locking in the newly developed mixed finite element models. In the nonlinear analysis, convergences of nonlinear finite element solutions of newly developed mixed finite element models are presented along with those of existing traditional model to compare the performance. تفاصيل المقالة