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Numerical modeling with treatment of trimmed objects such as internal cutouts in terms of NURBS-based isogeometric analysis presents several challenges, primarily due to the tensor product of the NURBS basis functions. In this paper we develop a new simple and effective isogeometric analysis for modeling buckling and free vibration problems of thin laminated composite plates with cutouts. We adopt the classical plate theory for the present formulation. The new approach can nicely overcome the drawbacks in modeling complex geometries with multiple-patches as the level sets are used to describe the internal cutouts; while the numerical integration is used only inside the physical domain. Numerical examples with complicated shapes are considered and analyzed to show the influences of cutout geometry, fiber orientation, boundary conditions, etc. on natural frequency and buckling behaviors of laminated plates. The results are compared with reference solutions showing a high accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Stacking sequence design is indispensable to make efficient use of the material properties of laminated composite materials. These laminated composites are usually fabricated from unidirectional plies of given thickness with fiber orientations limited to a small set of angles (e.g., 0°, +45°, –45°, and 90°). This leads to a combinatorial optimisation problem, which is rather complex to solve. In this paper, a new multi-population-based harmony search algorithm with dynamic interaction of populations, hybridised with a customised neighborhood algorithm to solve the layup sequence design problem of laminate composite plate is presented. Numerical experiments have been carried out by first considering the buckling and failure load optimisation of a laminate composite plate and later studies have been carried out using hybrid laminate plates for maximisation of buckling load and fundamental frequency with varied levels of hybridisation and for various plate aspect ratios. Numerical studies carried out in this paper clearly indicate that proposed dynamic hybrid adaptive harmony search algorithm is an effective combinatorial optimisation tool for stacking sequence optimisation of laminate composite structures and the computational performance is found to be superior when compared to other popular implementations of harmony search algorithm. [ABSTRACT FROM PUBLISHER]

A mathematical formulation is given of nonlinear axisymmetric buckling problems for plates and shells in the two-phase zones of austenite-to-martensite transformation. Numerical solutions of the direct-and inverse-transformation problems are used to construct hysteresis loops for thermomechanically cycled, pressure-loaded circular plates and shallow spherical domes of titanium nickelide (NiTi) alloy. It is shown that dynamic instability of the dome deformation process can occur during transformation under loads notably lower than the upper critical values for the isothermal states of the material outside the transformation zone. A theoretical analysis gives external loads below which the dome remains stable in the thermally cycled material with phase transformations. [ABSTRACT FROM AUTHOR]

The axisymmetric strain problem for a shell in the direct phase transformation interval is formulated approximately as a nonlinear boundary-value thermoelastic problem with an implicit temperature dependence (through a phase parameter simulating the volume fraction of the new-phase crystals). The buckling problems for a circular plate and a shallow spherical dome of TiNi alloy loaded by normal pressure in the direct phase transformation interval are solved numerically. The branches of buckled equilibrium states are obtained for various values of the loading and phase parameters. It is found that the deflections increase abruptly with an increase in the phase parameter for a fixed value of the loading parameter. The evolution of the buckling modes and the phase-strain distribution along the meridian are studied. [ABSTRACT FROM AUTHOR]

The problem of a rod and a plate subjected to plane strain in the interval of the direct phase transformation is formulated as a nonlinear boundary-value thermoelastic problem with an implicit dependence on temperature (through a phase parameter simulating the volume fraction of new-phase crystals). An analytical solution of the problem of a rod bent into a ring and a plate bent into a tube as a result of phase strains under the action of a small end bending moment is given. A numerical analysis of the buckling problem of a titanium nickelide (alloy) rod (plate) under longitudinal compression in the interval of the direct phase transformation shows that buckling becomes possible if the compressive load is much lower than the Euler critical load calculated before the transformation. Branches of buckled equilibrium states corresponding to loads lower than the Euler load are plotted as functions of the phase parameter. In all cases considered, the deflections increase abruptly in the neighborhood of the critical points. The evolution of buckling modes is studied, and the phase-strain distributions along the rod (plate) are shown. [ABSTRACT FROM AUTHOR]