The article proposes a method developed for model order reduction in a Finite Element (FE) framework that is capable of computing higher order stiffness tensors. In the method, a truncated third order asymptotic expansion is used for transformation of an FE model to a reduced system. The basis matrix in the formulation of the reduced-order model (ROM) is derived from linear mode shapes of the structure. The governing equations are derived using Hamilton's principle and the method is applied to geometrically nonlinear vibration problems to test its effectiveness. An initial validation of the numerical formulation is obtained by comparison of results from time domain nonlinear vibration analyses of a rectangular plate using Abaqus. Subsequently, a stiffened plate is modeled to test a more complex structure and a continuation algorithm is used in combination with the ROM to compute nonlinear frequency response curves. The validation of the stiffened plate has been performed through comparisons with the results of nonlinear vibration experiments. The experiments are conducted with Polytec Laser Doppler Vibrometer and PAK MK-II measurement systems for large amplitude vibrations to validate the nonlinear vibration analyses.@en

Traditional failure criteria for composites are usually formulated in material coordinates and depend on all three inplane stresses, hence failure evaluation depends on the ply angle. The omnistrain failure envelope describes the most critical failure envelope in strain space irrespective of ply orientation. This independence of ply orientation leads to an isotropic failure criterion that depends only on the principal strains. Omnistrain envelopes greatly simplify the task of design and optimisation of composite laminates. This paper proposes a numerical technique to generate omnistrain failure envelopes for different composite failure criteria. The failure index, describing how far a point in strain space is from the failure boundary, is used to describe the failure surface. Assuming convexity of the failure surface, a set of points is generated on the surface, and the convex hull algorithm is used to generate a polygonal approximation of the failure surface. Representing strains in terms of principal strains and the angle between the principal and material coordinates, allows us to eliminate the angle analytically by considering the worst case condition. The omnistrain envelope is thus directly generated from the approximate three-dimensional failure surface. The proposed algorithm does not require analytic expressions of the failure surface. An adaptive algorithm is proposed to generate the omnistrain envelope with relatively small number of points. As demonstration of the proposed algorithm, the omnistrain envelopes for various composite materials are generated for a number of composite failure criteria. The omnistrain envelopes generated for the Tsai-Wu criteria accurately match to existing analytic expressions.@en