A method of limit point calculation in finite element structural analysis

An approach is presented for the calculation of limit points for structures described by discrete coordinates, and whose governing equations derive from finite element concepts. The nonlinear load-displacement path of the imperfect structure is first traced by use of a direct iteration scheme and the determinant of the governing algebraic equations is calculated at each solution point. The limit point is then established by extrapolation and imposition of the condition of zero slope of the plot of load vs. determinant. Three problems are solved in illustration of the approach and in comparison with alternative procedures and test data

A finite element procedure for nonlinear prebuckling and initial postbuckling analysis

A procedure cast in a form appropriate to the finite element method is presented for geometrically nonlinear prebuckling and postbuckling structural analysis, including the identification of snap-through type of buckling. The principal features of this procedure are the use of direct iteration for solution of the nonlinear algebraic equations in the prebuckling range, an interpolation scheme for determination of the initial bifurcation point, a perturbation method in definition of the load-displacement behavior through the postbuckling regime, and extrapolation in determination of the limit point for snap-through buckling. Three numerical examples are presented in illustration of the procedure and in comparison with alternative approaches

A new hyperbolic-polynomial higher-order elasticity theory for mechanics of thick FGM beams with imperfection in the material composition

A drawback to the material composition of thick functionally graded materials (FGM) beams is checked out in this research in conjunction with a novel hyperbolic-polynomial higher-order elasticity beam theory (HPET). The proposed beam model consists of a novel shape function for the distribution of shear stress deformation in the transverse coordinate. The beam theory also incorporates the stretching effect to present an indirect effect of thickness variations. As a result of compounding the proposed beam model in linear Lagrangian strains and variational of energy, the system of equations is obtained. The Galerkin method is here expanded for several edge conditions to obtain elastic critical buckling values. First, the importance of the higher-order beam theory, as well as stretching effect, is assessed in assorted tabulated comparisons. Next, with validations based on the existing and open literature, the proposed shape function is evaluated to consider the desired accuracy. Some comparative graphs by means of well-known shape functions are plotted. These comparisons reveal a very good compliance. In the final section of the paper, based on an inappropriate mixture of the SUS304 and Si3C4 as the first type of FGM beam (Beam-I) and, Al and Al2O3 as the second type (Beam-II), the results are pictured while the beam is kept in four states, clamped–clamped (C–C), pinned–pinned (S–S), clamped-pinned (C–S) and in particular cantilever (C–F). We found that the defect impresses markedly an FGM beam with boundary conditions with lower degrees of freedom

An efficient mixed variational reduced order model formulation for non-linear analyses of elastic shells

The Koiter-Newton method had recently demonstrated a superior performance for non-linear analyses of structures, compared to traditional path-following strategies. The method follows a predictor-corrector scheme to trace the entire equilibrium path. During a predictor step a reduced order model is constructed based on Koiter's asymptotic post-buckling theory which is followed by a Newton iteration in the corrector phase to regain the equilibrium of forces. In this manuscript, we introduce a robust mixed solid-shell formulation to further enhance the efficiency of stability analyses in various aspects. We show that a Hellinger-Reissner variational formulation facilitates the reduced order model construction omitting an expensive evaluation of the inherent fourth order derivatives of the strain energy. We demonstrate that extremely large step sizes with a reasonable out-of-balance residual can be obtained with substantial impact on the total number of steps needed to trace the complete equilibrium path. More importantly, the numerical effort of the corrector phase involving a Newton iteration of the full order model is drastically reduced thus revealing the true strength of the proposed formulation. We study a number of problems from engineering and compare the results to the conventional approach in order to highlight the gain in numerical efficiency for stability problems

On materially and geometrically non-linear analysis of reinforced concrete planar frames

A family of new beam finite elements for geometrically and materially non-linear static analysis of reinforced concrete planar frames is derived, in which strain measures are the only interpolated unknowns, and where the constitutive and equilibrium internal forces are equal at integration points. The strain-localization caused by the strain-softening at cross-sections is resolved by the introduction of a `short constant-strain element'. Comparisons between numerical and experimental results on planar frames in pre- and post-critical states show both good accuracy and computational efficiency of the present formulation. (C) 2004 Elsevier Ltd. All rights reserved

Vibration and buckling of open TWBs with local weakening

Free vibration and Ljapounov stability of compressed open thin-walled beams with a cross-section reduction are studied by a in-house finite differences numerical code, based on a refined direct beam model and allowing for investigating elastic stability of non-trivial equilibrium paths in a dynamic setting. The benchmark is a beam with doubly symmetric cross-section and non-zero warping rigidity, under free, semi-, and fully restrained warping at its ends. In all cases, the results of the direct model are compared to finite element and/or experimental ones. The reduction in the cross-section rigidity induces a weakening that may model a local damage; thus, the present investigation may be useful with an outlook to damage monitoring and identification

Synthetic models for the analysis and control of composite and sandwich aerospace structures in critical conditions

L'abstract è presente nell'allegato / the abstract is in the attachmen

Phase conjugation method and apparatus for an active retrodirective antenna array

An active retrodirective antenna array wherein a reference array element is used to generate a phase reference which is replicated at succeeding elements of the array. Each element of the array is associated with a phase regeneration circuit and the phase conjugation circuitry of an adjacent element. In one implementation, the phase reference circuit operates on the input signal at the reference element, a voltage controlled oscillator (VCO) output signal and the input pilot signal at the next array element received from a transmission line. By proper filtering and mixing, a phase component may be produced to which the VCO may be locked to produce the phase conjugate of the pilot signal at the next array element plus a transmission line delay. In another implementation, particularly suited for large arrays in space, two different input pilot frequencies are employed