Michael P. Nemeth

Importance of anisotropy on buckling of compression-loaded symmetric composite plates

The differential equation governing buckling of symmetrically laminated composite plates loaded in compression is presented in nondimensiona l form. From this equation, nondimensional material coefficients are obtained, and a nondimensional parameter is presented that is used to assess when anisotropic bending stiffnesses can be neglected in a buckling analysis. Results obtained using finite element analyses are presented that show how boundary conditions, aspect ratio, fiber orientation, stacking sequence, and thickness affect the importance of the anisotropic bending stiffnesses.

Buckling behavior of compression-loaded symmetrically laminated angle-ply plates with holes

An approximate analysis for buckling of a rectangular specially-orthotropic plate with a central circular hole is applied to symmetrically-laminated angle-ply plates. Results obtained from finite element analyses and experiments indicate that the approximate analysis predicts accurately the buckling loads of (+/-theta sub m)s plates with integer values of m not below 6 and with hole diameters up to 50 percent of the plate width. Moreover, the results indicate that the approximate analysis can be used to predict the buckling trends of plates with hole diameters up to 70 percent of the plate width. Results of a parametric study indicate the influence of hole size, plate aspect ratio, loading conditions, boundary conditions, and orthotropy on the buckling load. Results are also presented that indicate the relationship of the bending stiffness and the prebuckling load distribution to the buckling load of a plate with a hole.

Shell Buckling Design Criteria Based on Manufacturing Imperfection Signatures

An analysis-based approach for developing shell-buckling design criteria for laminated-composite cylindrical shells that accurately account for the effects of initial geometric imperfections is presented. With this approach, measured initial geometric imperfection data from six graphite-epoxy shells are used to determine a manufacturing-process-specific imperfection signature for these shells. This imperfection signature is then used as input into nonlinear finite element analyses. The imperfection signature represents a first-approximation mean imperfection shape that is suitable for developing preliminary-design data. Comparisons of test data and analytical results obtained by using several different imperfection shapes are presented for selected shells. These shapes include the actual measured imperfection shape of the test specimens, a first-approximation mean imperfection shape, with and without plus or minus one standard deviation, and the linear-bifurcation-mode imperfection shape. In addition, buckling interaction curves for composite shells subjected to combined axial compression and torsion loading are presented that were obtained by using the various imperfection shapes in the analyses. A discussion of the nonlinear finite element analyses is also presented. Overall, the results indicate that the analysis-based approach presented for developing reliable preliminary-design criteria has the potential to provide improved, less conservative buckling-load estimates and to reduce the weight and cost of developing buckling-resistant shell structures.

Micropolar beam models for lattice grids with rigid joints

Abstract A simple, rational approach is presented for developing micropolar beam models for large repetitive beam-like planar lattices with rigid joints. The micropolar beam models have independent microrotation, and displacement fields and are characterized by their strain and kinetic energies, from which the equations of motion and boundary conditions can be derived. The procedure for developing the expression for the strain energy of the micropolar beam involves introducing basic assumptions regarding the variation of the displacement and microrotation components in the plane of the cross-section and obtaining effective elastic coefficients of the continuum in terms of the material properties and geometry of the original lattice structure. The high accuracy of the solutions obtained by the micropolar beam models is demonstrated by means of numerical examples.

Analysis of spatial beamlike lattices with rigid joints

Abstract Micropolar beam models are developed for the static, free vibration and buckling analysis of repetitive spatial beamlike lattices with rigid joints. The micropolar beam models have independent microrotation and displacement fields and are characterized by their strain energy, potential energy due to initial stresses and kinetic energy from which the governing differential equations and boundary conditions can be derived. The procedure for developing the expression for the strain energy of the micropolar beam involves introducing basic assumptions regarding the variation of the displacement and microrotation components in the plane of the cross-section, and obtaining effective elastic coefficients of the continuum in terms of the material properties and geometry of the original lattice structure. The high accuracy of the solutions obtained by the micropolar beam models is demonstrated by means of numerical examples for vierendeel and double-laced lattice girders with triangular cross-sections.

Improved Design Formulae for Buckling of Orthotropic Plates under Combined Loading

Simple, accurate buckling interaction formulae are presented for long orthotropic plates with either simply supported or clamped longitudinal edges and under combined loading that are suitable for design studies. The loads include 1) combined uniaxial compression (or tension) and shear, 2) combined pure inplane bending and 3) shear and combined uniaxial compression (or tension) and pure inplane bending. The interaction formulae are the results of detailed regression analysis of buckling data obtained from a very accurate Rayleigh-Ritz method.

Buckling of symmetrically laminated plates with compression, shear, and in-plane bending

A parametric study of the buckling behavior of infinitely long symmetrically laminated anisotropic plates subjected to combined loadings is presented. The loading conditions considered are pure in-plane bending, transverse tension and compression, and shear. Results obtained using a special purpose analysis that is well suited for parametric studies are presented for clamped and simply supported plates. Moreover, results are presented for some common laminate constructions, and generic buckling design charts are presented for a wide range of useful nondimensional parameters.

On a High-Fidelity Hierarchical Approach to Buckling Load Calculations

A step towards developing a new design philosophy for buckling-critical thinwalled shells is described. This new design philosophy is intended to advance thinwalled shell design technology from the traditional empirical design approach used today towards a science-based design-technology approach. This science-based design-technology approach is based on the hierarchical “high-fidelity-analysis” approach to buckling load calculations proposed by Arbocz et al. [1] where the uncertainties involved in a design are simulated by refined and accurate numerical methods. This hierarchical analysis approach includes three levels of shell buckling analyses that range from classical linear bifurcation buckling analysis (Level-1 analysis) to nonlinear finite element collapse analysis (Level-3 analysis) to provide an accurate prediction of the critical buckling load of a given shell structure. The critical buckling load and the estimated imperfection sensitivity of the shell are verified using a sufficiently refined finite element model with current generation two-dimensional shell analysis codes that include both geometric and material nonlinearities. The new approach is demonstrated for a quasi-isotropic composite shell [2].

A complex potential-variational method for stress analysis of unsymmetric laminates with an elliptical cutout

A combined complex potential-variational solution method is developed for the analysis of unsymmetrically laminated plates with finite planform geometry, subjected to arbitrary edge loads, and with an inclined elliptical cutout. This method uses complex potentials and their Laurent series expansions to reduce the potential energy of a plate to a contour integral that is evaluated numerically by the trapezoidal rule. A variational statement of equilibrium is applied to the potential energy to obtain a linear system of equations in terms of the unknown coefficients of the Laurent series, whose solutions yield the stress and displacement fields for a given problem. This approach represents a computationally efficient alternative to boundary collocation procedures that are typically used to solve problems based on complex potential theory. Comparisons are made with corresponding results obtained from finite element analysis for a square unsymmetrically laminated plate with a central inclined elliptical cutout and subjected to biaxial tension. The results confirm the validity of the solution method.

A Hierarchical Approach to Buckling Load Calculations

The advantages of using a hierarchical analysis approach to calculate the buckling load of an axially compressed composite cylindrical shell is demonstrated using an example taken from a recent experimental program. The Delft Interactive Shell DEsign COde (DISDECO) shell design code is used for this hierarchical analysis approach to provide an accurate prediction of the critical buckling load of the actual shell structure. DISDECO includes the influence of the boundary conditions, initial geometric imperfections, the effects of stiffener and load eccentricities, and the effects of prebuckling deformations caused by edge constraints in the analysis. It is shown that the use of DISDECO makes it relatively simple to proceed step by step from simple to more complex models and solution procedures. As a final step in the hierarchical analysis approach, the critical buckling load and the estimated imperfection sensitivity of the shell are verified by conducting an analysis of a large finite element model with one of the current generation two-dimensional shell analysis codes with advanced capabilities needed to represent both geometric and material nonlinearities.