Norman F. Knight

Optimal Design of General Stiffened Composite Circular Cylinders for Global Buckling with Strength Constraints

A design strategy for optimal design of composite grid-stiffened cylinders subjected to global and local buckling constraints and strength constraints was developed using a discrete optimizer based on a genetic algorithm. An improved smeared stiffener theory was used for the global analysis. Local buckling of skin segments were assessed using a Rayleigh-Ritz method that accounts for material anisotropy. The local buckling of stiffener segments were also assessed. Constraints on the axial membrane strain in the skin and stiffener segments were imposed to include strength criteria in the grid-stiffened cylinder design. Design variables used in this study were the axial and transverse stiffener spacings, stiffener height and thickness, skin laminate stacking sequence and stiffening configuration, where stiffening configuration is a design variable that indicates the combination of axial, transverse and diagonal stiffener in the grid-stiffened cylinder. The design optimization process was adapted to identify the best suited stiffening configurations and stiffener spacings for grid-stiffened composite cylinder with the length and radius of the cylinder, the design in-plane loads and material properties as inputs. The effect of having axial membrane strain constraints in the skin and stiffener segments in the optimization process is also studied for selected stiffening configurations.

Buckling of arbitrary quadrilateral anisotropic plates

The problem of buckling of arbitrary quadrilateral anisotropic plates with different boundary conditions under combined in-plane loading is considered. A Rayleigh-Ritz method combined with a variational formulation and a first-order transverse-shear-deformation theory is used. The Ritz functions consist of polynomials which include «circulation» functions that impose various boundary conditions. Numerical results are obtained for isotropic, orthotropic, and anisotropic plates with skewed geometries and are compared with existing results that use series solutions and with results generated from finite element simulations

An assessment of shell theories for buckling ofcircular cylindrical laminated composite panels loaded inaxial compression

Abstract Buckling loads of circular cylindrical laminated composite panels are obtained usingSanders–Koiter (e.g. Sanders, 1959 ; Koiter, 1959 ) , Love (e.g. Love, 1927 ) and Donnell (e.g. Loo, 1957 ) shell theories with a first-order, shear-deformationapproach and a Rayleigh–Ritz method that accounts for different boundary conditions andmaterial anisotropy. Results obtained using Sanders–Koiter, Love, Donnell shell theories arecompared with those obtained from finite element simulations, where the curved panels aremodeled using nine-node quadrilateral continuum-based shell elements that are independent of anyshell theory. Comparisons with finite element results indicate that Donnells theory could be inerror for some lamination schemes and geometrical parameters.

A refined first-order shear-deformation theory and its justification by plane strain bending problem of laminated plates

Abstract A refined first-order shear-deformation theory is proposed and used to solve the plane strain bending; problem of both homogeneous plates and symmetric cross-ply laminated plates. In Reissner-Mindlins traditional first-order shear-deformation theory (FSDT), the displacement field assumptions include a linear inplane displacement component and a constant transverse deflection through the thickness. These assumptions are retained in the present refined theory. However, the associated transverse shear strain derived from these displacement assumptions, which is still independent of the thickness coordinate, is endowed with new meaning—the stress-weighted average shear strain through the thickness. The variable distribution of transverse shear strain is assumed in such a way that it agrees with the shear stress distribution derived from the integration of equilibrium equation. This paper introduces the effective transverse shear stiffness of plates by assuming that the normalized distribution of through-the-thickness transverse shear stress remains unchanged regardless of geometrical configuration (span-to-thickness ratio) for plane-strain bending problem, which is justified by the exact elasticity solution. Without losing the simplicity of the displacement field assumptions of Reissner-Mindlins FSDT, the present refined first-order theory not only shows improvement on predicting deflections but also accounts for a variable transverse shear strain distribution through the thickness. In addition, all the boundary conditions, equilibrium equations, and constitutive relations are satisfied pointwise. Comparisons of deflection, transverse shear strain, and transverse shear stress obtained using the present theory are made with the exact results given by Pagano.

Formulation of an improved smeared stiffener theory for buckling analysis of grid-stiffened composite panels

An improved smeared stiffener theory for stiffened panels is presented that includes skin-stiffener interaction effects. The neutral surface profile of the skin-stiffener combination is developed analytically using the minimum potential energy principle and statics conditions. The skin-stiffener interaction is accounted for by computing the bending and coupling stiffness due to the stiffener and the skin in the skin-stiffener region about a shift in the neutral axis at the stiffener. Buckling load results for axially stiffened, orthogrid, and general grid-stiffened panels are obtained using the smeared stiffness combined with a Rayleigh-Ritz method and are compared with results from detailed finite element analyses.

Optimal Design of Grid-Stiffened Composite Panels

A design strategy for optimal design of composite grid-stiffened panels subjected to global and local buckling constraints is developed using a discrete optimizer. An improved smeared stiffener theory is used for the global buckling analysis. Local buckling of skin segments is assessed using a Rayleigh-Ritz method that accounts for material anisotropy and transverse shear flexibility. The local buckling of stiffener segments is also assessed. Design variables are the axial and transverse stiffener spacing, stiffener height and thickness, skin laminate, and stiffening configuration, where the stiffening configuration is herein defined as a design variable that indicates the combination of axial, transverse, and diagonal stiffeners in the stiffened panel. The design optimization process is adapted to identify the lightest-weight stiffening configuration and stiffener spacing for grid-stiffened composite panels given the overall panel dimensions, in-plane design loads, material properties, and boundary conditions of the grid-stiffened panel.

Restatement of first-order shear-deformation theory for laminated plates

Abstract A restatement of the first-order shear-deformation theory of plates is offered and verified numerically by exact 3-D elasticity results. Based on a more appropriate physical assumption, the restated theory innovatively interprets its variables and applies elasticity equations in a more pertinent manner. It assumes physically that only in some average sense does a straight line originally normal to the midplane remain straight and rotate relative to the normal of the midplane after deformation. Hence the in-plane displacement is still approximated, in an average sense, as linear and the transverse deflection as constant through the plate thickness. The associated nominal-uniform transverse shear strain directly derived from these displacement field assumptions is identified as the weighted-average transverse shear strain through the plate thickness, with the corresponding transverse shear stress as the weighting function, while the actual transverse shear strain is permitted to vary through the thickness and satisfies the constitutive law with its stress counterpart. Likewise, the average rotation of the line is identified as its weighted-average value, instead of the one evaluated from a linear regression of the inplane displacement with the least-square method. Examination of bending energy and transverse shear energy supports this interpretation. In addition, an effective transverse shear stiffness parameter is identified and proven appropriate. This restated first-order, shear-deformation theory yields accurate local as well as global response predictions without employing a shear-correction factor.

Buckling analysis of general triangular anisotropic plates using polynomials

The problem of buckling of general triangular anisotropic plates with different boundary conditions subjected to combined in-plane loads is considered. Solutions for plate buckling are obtained by using a Rayleigh-Ritz method combined with a variational formulation. The Ritz functions consist of polynomials that include circulation functions that are used to impose various boundary conditions. Both classical laminated-plate theory and first-order shear-deformation theory are used. Numerical buckling results obtained for isotropic and anisotropic triangular plates are compared with results from existing series solutions.

On a consistent first-order shear-deformation theory for laminated plates

Abstract This paper systematically states the consistent first-order shear-deformation theory for laminated plates recently proposed by Qi and Knight. It assumes that only in an average sense does a straight line originally normal to the midplane remain straight and rotate relative to the normal of the midplane, and in a local sense a slight displacement perturbation around the average rotated line is also permitted after deformation. Since the curved line is very shallow, the present theory still approximates linear in-plane and constant transverse displacements through the thickness just as Reissner and Mindlins first-order shear-deformation theory does. Reissner and Mindlins theory leads to uniform transverse shear strain distributions by employing pointwise strain displacement relationships, and satisfies the transverse shear constitutive relationships only in an average corrected form. In contrast, Qi and Knights theory accounts for variable transverse shear strain distributions by enforcing pointwise constitutive relationships, and relates transverse shear strains to kinematic unknowns only in a weighted-average form. Through-the-thickness transverse shear strains are thus consistent with the stress counterparts and their transverse-shear-stress-weighted-average values are just the nominal-uniform transverse shear strains which correspond to the average rotations. The new theory combines the advantages of several prevailing 2D laminated plate theories while overcoming their drawbacks. Numerical results for the cylindrical bending problem of orthotropic laminated plates exhibit excellent agreement between Qi and Knights theory and Paganos 3D exact elasticity results.

NON-LINEAR STRUCTURAL RESPONSE USING ADAPTIVE DYNAMIC RELAXATION ON A MASSIVELY PARALLEL-PROCESSING SYSTEM

A parallel adaptive dynamic relaxation (ADR) algorithm has been developed for nonlinear structural analysis. This algorithm has minimal memory requirements, is easily parallelizable and scalable to many processors, and is generally very reliable and efficient for highly nonlinear problems. Performance evaluations on single-processor computers have shown that the ADR algorithm is reliable and highly vectorizable, and that it is competitive with direct solution methods for the highly nonlinear problems considered. The present algorithm is implemented on the 512-processor Intel Touchstone DELTA system at Caltech, and it is designed to minimize the extent and frequency of interprocessor communication. The algorithm has been used to solve for the nonlinear static response of two and three dimensional hyperelastic systems involving contact. Impressive relative speedups have been achieved and demonstrate the high scalability of the ADR algorithm. For the class of problems addressed, the ADR algorithm represents a very promising approach for parallel-vector processing.