Sherrill B. Biggers

The order of stress singularities for bonded and disbonded three-material junctions

Abstract In-plane solutions are given for the order of the stress singularity at an internal point in an elastic, isotropic solid where three wedges of different materials meet. The three interfaces are either all perfectly bonded or a disbond is introduced along one interface. One feature of this three-material junction that is not present for the corresponding two-material case, is that each interface is geometrically different and, therefore, the singular behavior is dependent on which interface is disbonded. Each material and geometrical combination therefore gives rise to four problems, one with perfect bonding at all interfaces, and three cases of an interface disbond. Numerical results are presented for selected three-material junctions. New results for two-material junctions and wedges that serve as special cases for the present study are also presented.

A finite element approach to three-dimensional singular stress states in anisotropic multi-material wedges and junctions

Abstract A finite element formulation is developed to determine the order and angular variation of singular stress states due to material and geometric discontinuities in anisotropic materials. The formulation applies to any two-dimensional geometry that is prismatic in the third direction and has three-dimensional displacement fields. In some special cases the three-dimensional fields become uncoupled antiplane and inplane fields and this formulation yields the uncoupled results. The formulation provides for the determination of the asymptotic stress and displacement fields present at interior singular points of three-dimensional structures. The displacement field of the sectorial finite element is quadratic in the angular coordinate direction and asymptotic in the radial direction measured from the singular point. The formulation of Yamada and Okumura [(1983) Hybrid and Mixed Finite Element Methods , pp. 325–343. Wiley, Chichester] for inplane problems is adapted for this purpose. The simplicity and accuracy of the formulation are demonstrated by comparison with several analytical solutions for both isotropic and anisotropic multi-material wedges and junctions. The nature and speed of convergence associated with the element suggests that it could be employed in developing two-dimensional and three-dimensional enriched elements for use along with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries leading to singular stress states.

Finite element analysis of anisotropic materials with singular inplane stress fields

Abstract A finite element formulation is developed for the analysis of singular stress states at material and geometric discontinuities in anisotropic materials loaded inplane. The displacement field of the sectorial element is quadratic in the angular coordinate direction and exponential in the radial direction measured from the singular point. The formulation of Yamada and Okumura (1983a, b) is extended to take into account the anisotropy of the material. The stress and displacement fields are obtained when the order of the stress singularity is real as well as complex. When the order of the stress singularity is complex, it is shown that the angular variation of the stress and displacement fields can be expressed in an infinite number of ways. Results for the displacement and stress fields obtained when the order of the stress singularity is complex can be made to match already published results once a similarity transformation is applied. The simplicity and accuracy of the formulation are demonstrated by comparison to several analytical solutions for both isotropic and anisotropic multi-material wedges and junctions with and without disbonds. The nature and rate of convergence associated with the element suggests that it could be used in developing enriched elements for use with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries.

Compression Buckling Response of Tailored Rectangular Composite Plates

Buckling resistance is often a controlling criterion in the design of structures composed of plate elements. Design concepts that lead to increased buckling loads (or strains) of these plate elements can directly lower the structural cost and/or weight by a number of means. This study quantifies the improvements that can be achieved in compression buckling loads of rectangular composite plates by using a simple stiffness-tailoring concept. The approach is to position the unidirectional lamina through the thickness and over the planform of the plate so that the buckling load is increased with no loss in in-plane stiffness or increase in weight. Finite element analyses have been used to determine the effects of tailoring on the buckling loads of plates with various boundary conditions, aspect ratios, thicknesses, and membrane stiffnesses. Increases in buckling loads (or strains) of 200% or more compared to the uniform plate-buckling loads are shown possible with this tailoring concept. HE design of aircraft primary structural elements is often strongly influenced by a plate-buckling criterion. For ex- ample, the wing cover surface is normally restricted from buckling at loads up to maximum operating or even ultimate levels due to aerodynamic smoothness or global stiffness re- quirements. The fuselage skin is often restricted from buckling up to a relatively low load level to control out-of-plane defor- mations at normal service conditions and to limit these defor- mations and the loss of effective in-plane stiffnesses at higher postbuckling load levels. Similar requirements exist for struc- tural elements in many other types of applications. Design concepts that lead to increased plate-buckling loads (or strains) can directly lower the structural cost and/or weight by 1) allowing supporting substructure to be more widely spaced, thus reducing substructure, fastener, and attachment part count, 2) allowing the use of simpler substructure offering little rotational restraint to the surface structural elements, or 3) reducing the total structural weight by permitting design to a higher strain level governed by the material strength or damage tolerance rather than to lower values governed by buckling. This study quantifies the improvements that can be achieved in compression buckling loads of rectangular composite plates by using a simple stiffness-tailoring concept. It provides guide- lines that designers can use to achieve the improvement. Here stiffness tailoring is defined as the precise placement of lamina with various orientations through the thickness and across the planform of the laminated plate. The local membrane and bending stiffnesses of the tailored plate become nonuniform over the plate. When the loading is applied to the plate in the form of uniform imposed end displacements, stiffness tailor- ing brings about a redistribution of the in-plane loads that can directly benefit buckling response. At the same time, the dis- tribution and magnitudes of the bending and twisting stiff- nesses can also be modified to further improve the buckling load. The properly tailored design will be a function of the type of loading, the plate geometry, the boundary conditions, the relative material properties, and the basic configuration of the tailoring concept. Bulson1 shows that the type of tailoring

Postbuckling analysis with progressive damage modeling in tailored laminated plates and shells with a cutout

Abstract An approach to modeling inplane damage progression in postbuckled laminated composite panels is shown to be accurate by comparison to experimental test data from other sources. A simple tailoring concept is shown to be very effective in increasing compressive buckling loads and ultimate loads for flat plates and curved panels with a central cutout. Effects of cutout size, the degree of tailoring, and inplane restraint on the unloaded edges are investigated. Optimal tailoring produces relative improvements in the flat plates ranging from 40% to 175% in buckling load and 190–240% in ultimate load capacity when compared to uniform plates with the same cutout sizes. In the curved panels, tailoring lowers the imperfection sensitivity and in some cases produces ultimate loads greater than the theoretical undamaged buckling loads. To the contrary, the ultimate load for the uniform curved panel is much lower than the undamaged buckling load. Relative improvements in ultimate loads range from a low of about 40% to a high of about 155% compared to uniform curved panels. Large differences in the damage initiation locations and damage progression patterns are shown between the flat and the curved panels. In summary, the tailoring concept investigated here can provide excellent improvements in ultimate load capacity in flat and curved panels with the largest benefits occurring in thin flat panels that are loaded far into the compressive postbuckling regime.

Shear buckling response of tailored composite plates

This Note evaluates the piecewise-uniform approach to tailoring as a mean of improving the shear buckling loads of composite plates. This design approach is referred to herein as stiffness tailoring or, more simply, as tailoring. The primary objectives are to determine the tailoring patterns and the degree of concentration of the material used to achieve the tailoring in each pattern that maximize the shear buckling load and to quantify the maximum relative improvement that can be achieved in the buckling load compared to uniform plates.

Postbuckling analysis of tailored composite plates with progressive damage

Abstract Composite plates can be optimized to maximize their buckling and postbuckling resistance. A simple, piece-wise uniform, stiffness tailoring concept has previously been shown to increase buckling loads and improve postbuckling performance. In the present study, this stiffness tailoring concept is further investigated to determine its usefulness in increasing the ultimate postbuckling failure load of a composite plate. A simple material model is used to describe the material behavior with damage. Various configurations of plates are examined in the finite element postbuckling analysis with progressive damage. The results show that highly tailored composite plates can have ultimate failure loads 3–5 times higher than a corresponding uniform plate.

Identifying global/local interface boundaries using an objective search method

One of the key components in computational mechanics procedures using global/local methods is the specification of the global/local interface. Global/local interfaces are usually specified by visually examining some measure of response such as colour-coded contour plots of stresses or strain energy. However, when both global and local domains are modelled in three dimensions, such a specification is not as obvious, and it lacks objectivity and uniqueness. An Objective Search Method (OSM) is presented to specify the global/local interface in three dimensions in a precise, repeatable and automated manner. The OSM performs the search incrementally in all directions in three dimensions radiating from a location of interest until certain generalized guidelines are satisfied and the global/local interface is identified. The OSM is suited to problems where localized phenomena exist but where their domains are not known a priori. The generalized guidelines for the OSM require the identification of nodes lying on the external surfaces of the model. As an important component of the OSM, a unique method to identify surface nodes has been developed and is also presented. Finally, the uniqueness, sensitivity and versatility of the OSM is illustrated using two example problems and the computational effort involved with the OSM is discussed in the context of a third example problem.

Postbuckling Response of Piece-Wise Uniform Tailored Composite Plates in Compression

Tailoring, or precisely specifying, the types, amounts, orientations and locations of composite materials in a structure to satisfy specific performance require ments is inherent to the design of efficient composite structures. A simple piece-wise uni form stiffness tailoring concept has previously been shown to increase compressive buck ling loads of plates by as much as 138 % to 195% , depending on the baseline uniform laminate. The question arises as to what benefits, it any, exist for plates tailored in this way when loaded in the postbuckling regime. This paper presents predictions for global measures of the postbuckling response of plates loaded in compression which have been tailored to maximize the initial buckling load. The analysis shows that postbuckling loads at failure can be increased by 130% to 150% by tailoring. The edge strain at first-ply fail ure is not significantly affected by tailoring. Postbuckling membrane secant and tangent stiffnesses are much higher for tailored plates than for uniform plates. Out-of-plane postbuckling deflections are shown to be much smaller at a given load level when tailoring is employed. The initial buckling mode shape and the manner in which postbuckling mode changes take place are strongly affected by tailoring. Thus, with this design approach, op timization for initial buckling can provide concurrent benefits in postbuckling response. This improved performance suggests that the skin plate of stiffened composite panels could be tailored using the current approach to significantly improve the postbuckling perform ance of stiffened panels.

Structural response and relative strength of a laminated composite hip prosthesis: effects of functional activity.

To obtain a better appreciation for the structural performance of a laminated composite hip prosthesis (CP), we examined in situ prosthesis structural response and relative strengths as a function of walking and stair climbing using our previously developed analysis guidelines. Accordingly, we examined overall prosthesis structural response utilizing a global continuum level modeling approach and prosthesis relative strengths using a local microstructural (or ply-level) modeling approach. As a reference and control, we examined the structural performance of the intact natural femur (NAT) and a titanium alloy (Ti) based hip prosthesis. In terms of the overall structural response, i.e., the femur/prosthesis deformational response, stem/bone interfacial stress transfer, and calcar strain energy density restored, the performance of the CP prosthesis was moderately improved over that of the control Ti prosthesis and better approximates the NAT response. In terms of relative strength, we found that the neck of the CP prosthesis failed for all activities with the exception of the mid-stance phase of level walking. However, the prosthesis appears to have sufficient relative strength for function at positions distal to the neck of the prosthesis. While these results dampen enthusiasm for consideration of laminated composite hip prostheses designed with a shape based on a metal alloy implant, they indirectly support consideration of alternate hip prosthesis structural designs such as using a better supported prosthesis neck or utilizing metal/composite hybrid constructions. Importantly, our simulation and analysis approach could be utilized in the design of other laminated composite biomedical structural components.