Partial Edge Loading Research Articles

Vibration of Stiffened Plates with Cutout Subjected to Partial Edge Loading

The buckling and vibration characteristics of stiffened plates with cutout subjected to in-plane partial edge loadings at the plate boundary are studied using finite element method. Buckling loads and vibration frequencies are determined for different plate and cutout aspect ratios, various boundary conditions, partial edge loading at different locations, cutout ratios, various parameters of stiffeners by varying the number, size and location of the stiffeners. The analysis presented determines the stresses all over the region for different kinds of loading and edge conditions. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The buckling and vibration characteristics are discussed and the free vibration results available in the literature for stiffened plates with/without cutout are compared.

The Breathing of Webs Under Repeated Partial Edge Loading

Slender webs subjected to many times repeated partial edge loading repeatedly buckle (breathe) under this loading, which brings about the initiation and propagation of fatigue cracks in the neighbourhood of the loaded flange. This phenomenon leads to a significant “erosion” of the post-buckled behaviour of the web, which would very beneficially affect the limit state of the web if its loading were not repeated. Based on their experimental results, the authors establish user-friendly formulae such as to make it possible entirely to disregard the detrimental effect of web breathing even in the case of repeated loads, but on the condition that the maximum value of the cyclic loading is kept under a certain limit

Experimental and numerical studies on buckling of cracked thin-plates under full and partial compression edge loading

Buckling failure is a common occurrence in thin plates under compression loading, in particular when there are some imperfections such as openings and cracks. This form of failure can often precede strength failure. In this paper, experimental and numerical studies on the critical buckling load of cracked plates subjected to axial compression is carried out. For this purpose, the rectangular plates made by 1200A aluminum alloy with central inclined crack are considered. The effects of crack length and orientation, thickness of plates and plate aspect ratio are investigated experimentally and numerically. Effects of boundary conditions and loadings are also studied by considering different types of supports and loading such as partial edge acting forces and supports. Finally, the results of experiments are compared with the results of numerical methods.

Buckling analysis of laminated plates by wavelets

This paper addresses, for the first time, the buckling analysis of isotropic and laminated plates that are subjected to partial inplane edge loads by a first-order shear deformation theory. The numerical approach is based on collocation with wavelets. It is shown that the present method produces highly accurate critical loads and modes.

Dynamic instability of imperfect laminated sandwich plates with in-plane partial edge load

Dynamic instability of laminated sandwich plates having inter-laminar imperfections with in-plane partial edge loading is studied for the first time using an efficient finite element plate model. The plate model is based on a refined higher order shear deformation plate theory, where the transverse shear stresses are continuous at the layer interfaces with stress free conditions at plate top and bottom surfaces. A linear spring-layer model is used to model the inter-laminar imperfection by considering in-plane displacement jumps at the interfaces. Interestingly the plate model having all these refined features requires unknowns at the reference plane only. However, this theory requires C1 continuity of transverse displacement (w) i.e., w and its derivatives should be continuous at the common edges between two elements, which is difficult to satisfy arbitrarily in any existing finite element. To deal with this, a new triangular element developed by the authors is used in the present paper.

Stability analysis of composite plates under localized in-plane load

Stability characteristics of isotropic and composite plates subjected to partial or concentrated compressive edge loads are investigated here using a four-noded shear-flexible quadrilateral high-precision plate-bending element. A complete cubic polynomial shape function is used to interpolate the in-plane displacements for better accuracy in capturing the high-stress zone near the locally distributed edge load. The influences of location and distribution of in-plane edge compression on the buckling load of composite plates are studied. The nonlinear governing equations based on von Kármán's assumptions are solved by Newton–Raphson technique to get the hitherto unreported postbuckling equilibrium paths of partially loaded plates made of isotropic, symmetric, and unsymmetric laminates. Marguerre's shallow-shell theory is employed to study the effect of sinusoidal imperfection on the nonlinear behavior of composite plates under partial in-plane load.

Dynamic instability analysis of stiffened shell panels subjected to partial edge loading along the edges

The dynamic instability characteristics of stiffened shell panels subjected to partial in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners, respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover, the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented through convergence and comparison with the published results from the literature. The effects of parameters like loading type and shell geometry are considered in the dynamic instability analysis of stiffened panels subjected to non-uniform in-plane harmonic loads along the boundaries. The tension buckling aspect of the stiffened panels are also considered and the dynamic stability behavior due to tensile in-plane edge loading is studied for the concentrated load.

Vibration of composites and sandwich laminates subjected to in-plane partial edge loading

The free vibration of composites and sandwich laminates subjected to in-plane partial edge loading is studied. An efficient finite element model based on a refined higher order shear deformation plate theory is developed for the present purpose. In this theory, the transverse shear stresses are continuous at the layer interfaces with stress free conditions at plate top and bottom surfaces. It is interesting to note that the plate model having all these refined features requires unknowns at the reference plane only. However, this theory requires C 1 continuity of transverse displacement at the element edges, which is difficult to satisfy arbitrarily in any existing finite element. To deal with this, a new triangular element recently developed by the authors is used in the present paper.

Dynamic instability of laminated sandwich plates subjected to in-plane partial edge loading

The dynamic instability of laminated sandwich plates subjected to in-plane partial edge loading is studied for the first time using an efficient finite element plate model. The plate model is based on a refined higher order shear deformation plate theory, where the transverse shear stresses are continuous at the layer interfaces with stress free conditions at plate top and bottom surfaces. Interestingly the plate model having all these refined features requires unknowns at the reference plane only. However, this theory requires C 1 continuity of transverse displacement, which is difficult to satisfy arbitrarily in any existing finite element. To deal with this, a new triangular element developed by the authors is used in the present paper.

ANALYSIS OF IMPERFECT COMPOSITES AND SANDWICH LAMINATES SUBJECTED TO IN-PLANE PARTIAL EDGE LOADING

The static response of imperfect composites and sandwich laminates subjected to in-plane partial edge loading is studied. An efficient finite element model based on a refined plate theory is developed for the present purpose. In this theory, the transverse shear stresses are continuous at the layer interfaces along with stress free conditions at the top and bottom surfaces of the plate. The imperfection is considered in the form of in-plane displacement jumps at the layer interfaces, which is characterized by a linear spring-layer model. It is quite encouraging to note that the plate model having all these refined features requires unknowns only at the reference plane. However, this theory demands C1continuity of transverse displacement at the element edges, which is difficult to accommodate arbitrarily in any existing finite element. To deal with this problem a new triangular element developed by the authors is used in the present study.

Dynamic stability of stiffened plates with cutout subjected to harmonic in-plane partial edge loading

The dynamic instability characteristics of eccentrically stiffened plates with cutout subjected to harmonic in-plane partial edge loadings at the plate boundaries are studied using finite element method. The instability regions are determined for a wide range of excitation frequencies with different boundary condition, partial edge loading at different locations, cutout ratios and various parameters of stiffeners using Bolotin's method and Hill's infinite determinants by varying the number, size and location of the stiffeners. In the structural modeling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained.

Buckling of laminated sandwich plates subjected to partial edge compression

The buckling characteristics of sandwich plates having laminated stiff layers are studied for different types of partial edge loadings using a refined plate theory. With this plate theory, the through thickness variation of transverse shear stresses is represented by piecewise parabolic functions where the continuity of these stresses is satisfied at the layer interfaces by taking jumps in the transverse shear strains at the interfaces. The transverse shear stresses free condition at the plate top and bottom surfaces is also satisfied. It is quite interesting to note that this plate model having all these refined features requires unknown parameters only at the reference plane. To have a generality in the present analysis, finite element technique is adopted and it is carried out with newly developed triangular element, as existing finite elements cannot accommodate this plate model. So far, no solution exists in the literature for the problem of sandwich plate subjected to partial edge loading. The present analysis is first validated for the case of an isotropic plate subjected to partial edge compression and then it is extended to analyze sandwich plates. Few results are presented.

Vibration of imperfect composite and sandwich laminates with in-plane partial edge load

The free vibration of imperfect composite and sandwich laminates subjected to in-plane partial edge loading is studied. An efficient finite element model recently developed by the authors based on a refined plate theory is used for the present purpose. In this theory, the transverse shear stresses are continuous at the layer interfaces with stress free conditions at plate top and bottom surfaces. The imperfection is considered in the form of in-plane displacement jumps at the layer interfaces, which is characterized by a linear spring-layer model. It is very interesting to note that the plate model having all these refined features requires unknowns only at the reference plane. However, this theory demands C 1 continuity of transverse displacement at the element edges, which is difficult to satisfy arbitrarily in any existing finite element. A new triangular element developed by the authors is used to deal with the problem.

Dynamic instability characteristics of laminated composite plates subjected to partial follower edge load with damping

The study of vibration and dynamic instability behaviour of laminated composite plates subjected to partially distributed non-conservative follower forces is presented by using the finite element technique. The first-order shear deformation theory is used to model the plate, considering the effects of shear deformation and rotary inertia. The modal transformation technique is employed to the resulting equilibrium equation for subsequent analysis. Structural damping is introduced into the system in terms of equivalent viscous damping to study the significance of damping on stability characteristics. The effects of load width, boundary condition, aspect ratio, ply orientation, direction control of the load and damping parameters are considered for the stability behaviour of the plates. The results show that under follower loading, the system is susceptible to instability due to flutter alone or due to both flutter and divergence, depending on system parameters.

Critical buckling of longitudinally stiffened webs subjected to compressive edge loads

The resistance of steel plate girders subjected to concentrated load can be described using a strength curve, which includes a gradual transition from yielding to buckling depending on the slenderness ratio of the web. The slenderness is a function of the ratio of the yield resistance to the critical buckling load. This paper describes a methodology for the determination of buckling coefficients for longitudinally stiffened plate girders subjected to partial edge loading or concentrated loads. After an extensive parametric analysis, the optimum parameters that govern the change from a global buckling mode to a more local buckling mode were found. As in similar buckling problems, the results show that the location and the relative flexural/torsional rigidity of the stiffener are relevant parameters that govern the final buckling shape. Finally an expression for the buckling coefficient used to determine the critical buckling load for longitudinally stiffened girder webs is presented.

Dynamic instability of stiffened plates subjected to non-uniform harmonic in-plane edge loading

The dynamic instability characteristics of stiffened plates subjected to in-plane partial and concentrated edge loadings are studied using finite element analysis. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The method of Hill's infinite determinants is applied to determine the dynamic instability regions. Numerical results are presented to study the effects of various parameters, such as static load factor, aspect ratio, boundary conditions, stiffening scheme and load parameters on the principal instability regions of stiffened plates using Bolotin's method. The results show that location, size and number of stiffeners have a significant effect on the location of the boundaries of the principal instability region.

Tension buckling and dynamic stability behaviour of laminated composite doubly curved panels subjected to partial edge loading

This paper deals with the study of tensile buckling, vibration and dynamic stability behaviour of multilaminated curved panels subjected to uniaxial in-plane point and patch tensile edge loadings by using the finite element method. The effect of first order shear deformation theory is used to model the doubly curved panels. Numerical results have been established through convergence and comparison with the published data from the literature. The effects of load position, number of layers, lamination angles, thickness ratio, aspect ratio and shell geometries of the panel are considered in the analysis and results are discussed.

Buckling and vibration of stiffened plates subjected to partial edge loading

The buckling and vibration characteristics of stiffened plates subjected to in-plane partial and concentrated edge loadings are studied using finite element method. The initial stresses are obtained considering the pre-buckling conditions. Buckling loads and vibration frequencies are determined for different plate aspect ratios, edge conditions and different partial non-uniform edge loading cases. The non-uniform loading may also be caused due to the supports on the edges. The analysis presented determines the stresses all over the region for different kinds of loading and edge conditions. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The vibration characteristics are discussed and the results are compared with those available in the literature. Buckling results show that the stiffened plate is less susceptible to buckling for position of loading near the supported edges and near the position of stiffeners as well.

Parametric Resonance Characteristics of Laminated Composite Doubly Curved Shells Subjected to Non-Uniform Loading

The parametric resonance characteristics of laminated composite doubly curved panels subjected to various in-plane static and periodic compressive edge loadings, including partial and concentrated edge loading are studied using finite element analysis. The first order shear deformation theory is used to model the doubly curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to the Sander’s first approximation for doubly curved laminated shells, which can be reduced to Love’s and Donnell’s theories by means of tracers. The effects of number of layers, static load factor, side to thickness ratio, shallowness ratio, boundary conditions, degree of orthotropy, ply orientations and various load parameters on the principal instability regions of doubly curved panels are studied in detail using Bolotin’s method. Quantitative results are presented to show the effects of shell geometry, lamination details and load parameters on the stability boundaries. Results of plates and cylindrical shells are also presented as special cases and are compared with those available in the literature.

PARAMETRIC INSTABILITY OF DOUBLY CURVED PANELS SUBJECTED TO NON-UNIFORM HARMONIC LOADING

The parametric instability characteristics of doubly curved panels subjected to various in-plane static and periodic compressive edge loadings, including partial and concentrated edge loadings are studied using finite element analysis. The first order shear deformation theory is used to model the doubly curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to the Sander's first approximation for doubly curved shells, which can be reduced to Love's and Donnell's theories by means of tracers. The effects of static load factor, aspect ratio, radius-to-thickness ratio, shallowness ratio, boundary conditions and the load parameters on the principal instability regions of doubly curved panels are studied in detail using Bolotin's method. Quantitative results are presented to show the effects of shell geometry and load parameters on the stability boundaries. Results for plates and cylindrical shells are also presented as special cases and are compared with those available in the literature.