Elasto-plastic analysis of orthogonally stiffened plates with initial imperfections under uniaxial compression

In general, the stiffened plates consisting of steel plate elements are unavoidably accompanied by initial imperfections such as residual stresses and initial deflections, which have considerable effects on their ultimate strength. Therefore, it is needed for designing them to develop more rational method taking the ultimate strength influenced by initial imperfections into account rather than the conventional design method being on the basis of the linear elastic buckling theory.From this point of view, this study aims to evaluate rigorously the ultimate strength of orthogonally stiffened plate with initial imperfections under uniaxial in-plane compression. The elasto-plastic finite element method is applied to attain this purpose. By a happy combination of modal analytical technique and conventional finite element method, much reduction of the degree of freedom can be expected to be realized herewith. Some numerical calculations are performed by means of this rigorous method to examine the exactness of the analysis. Moreover, the numerical results are compared with the experimental ones.     

Elasto-plastic response of uniformly loaded sector plates: full-section yield model predictions and spread of plasticity

The governing equations for an elasto-plastic large deflection analysis of pressure loaded sector plates, based on the Ilyushin full-section yield criterion and the flow theory of plasticity, are presented. An outline of the solution of these equations using a finite difference implementation of the dynamic relaxation algorithm is given. Numerical results are presented for uniformly loaded slender and stocky sector plates with a 60° sector angle. In particular, first yield data are presented as well as the results of two parameter studies. The first study shows the effects of flexural and in-plane edge conditions on the deflections and stress resultants/couples at the centre of the sector plate and the second contrasts the spread of plasticity in slender sector plates with simply supported and clamped in-plane fixed edges.     

On the elasto-plastic large deflection response of stocky annular steel plates

An incremental full-range analysis for pressure loaded annular plates is presented in outline. Von Karman large deflection plate theory coupled with the Prandtl-Reuss associated flow rule and a layered Von Mises yield criterion form the cornerstones of the analysis. The numerical solution of the governing equations is achieved via a finite-difference implementation of the DR algorithm. The DR analysis is used to carry out a numerical parameter study of the full-range response of uniformly loaded stocky steel annular plates. The study is primarily concerned with the effects of the edge support conditions in controlling the response and dimensionless results for deflections, etc. are presented for a total of nine inner and outer edge condition combinations.     

A parametric study of the axisymmetric full-range response of thickness-tapered circular steel plates

The incremental equations governing the full-range axisymmetric flexural response of thickness-tapered circular plates and their numerical solution via a finite-difference implementation of the Dynamic Relaxation (DR) technique are briefly outlined. A computer implementation of the DR analysis is used to carry out a parametric study of the response of thickness-tapered plates subjected to uniform normal pressure loading. Dimensionless results (deflections etc.) spanning the practical range of linear thickness tapers are presented for simply supported and clamped, slender and stocky plates.     

An elasto-plastic damage model cast in a co-rotational kinematic framework for large deformation analysis of laminated composite shells

This paper presents an elasto-plastic damage model that is based on irreversible thermodynamics and internal state variable formalism for the analysis of multi-layered composites. The model is based on a damage surface that is defined in terms of an internal damage variable of energy, along with a set of rate-independent elasto-plastic constitutive equations defined in an effective stress–strain space. Employing the operator splitting methodology, a three-step predictor/multi-corrector algorithm is developed that includes an elastic predictor, a plastic corrector, and a damage corrector. The constitutive model is cast in a co-rotational kinematic framework for damage analysis in laminated plates and shells undergoing large deflections. Numerical examples are presented to demonstrate the accuracy and range of applicability of the proposed model.     

Computer generated elasto-plastic design data for pressure loaded circular plates

Two finite-difference computer programs for the non-axisymmetric elasto-plastic large deflection analysis of circular plates are described. One of the programs uses a constitutive model based on the Ilyushin full-section yield criterion, whereas the other uses the von Mises layered yield criterion. The programs have been used to model the full-range response including multi-stage unloading, of uniformly loaded circular plates with various boundary conditions for a range of slendernesses. From the computed results design charts of first yield over-pressure versus maximum and residual centre deflection have been compiled. A numerical example of the use of these charts in the design of an end closure to a cylindrical pressure vessel is presented. Finally, sample charts for ‘pre-dished’ plates are presented as an illustration of the further potential of these programs for design data generation.     

Nonlinear transient responses of initially stressed composite plates

The nonlinear transient response of initially stressed composite plates is investigated using the finite element method. A nine-node isoparametric quadrilateral element is developed to model laminated plates under initial deformation and initial stress according to the Mindlin plate theory and von Karman large deflection assumptions. In the time integration, the Newmark constant acceleration method in conjunction with an efficient and accurate iteration scheme is used. Numerical results for deflections and bending moments for isotropic and laminated plates are obtained.     

Large deflection analysis of skew plates by lumped triangular element formulation

A finite difference scheme with triangular mesh is presented for the analysis of skew plate problems with large deflections. The suggested formulation is independent of the boundary condition and uses energy principles to derive a set of nonlinear algebraic equations which are solved by using Newton-Raphson iterative method with incremental loading. The investigation is concerned with the behaviour of constant thickness clamped and simply supported isotropic skew plates with immovable edges and subjected to uniformly distributed transverse load. The effects of skew on plates with large deflections are investigated and comparisons are made with existing results; good agreement is shown.     

Elasto-plastic analysis of axisymmetric structures subject to arbitrary loads by hybrid-stress finite elements

A semi-analytic finite element method in conjuction with a hybrid-stress functional based on the initial stress approach is presented for elasto-plastic analysis. A three-dimensional solid element based on hybrid-stress model is also implemented for the elasto-plastic analysis. A procedure to compute the non-linear effects in terms of Fourier series in the hybrid-stress model is described. The accuracy and efficiency of the semi-analytic method is evaluated via numerical examples by comparing the solution with a full 3-D solution. The semi-analytic method is observed to be a viable alternative to 3-D analysis in elasto-plastic analysis of axisymmetric structures subject to arbitrary loads.     

A semi-analytical approach to elasto-plastic analysis of hollow spheres

The integral form of the analytical solution for the problem of an elasto-plastic hollow sphere subjected to uniform loads is presented. This integral equation is solved through a numerical integration scheme involving an iteration technique. The numerical model developed on this basis is shown to satisfy the theoretical solution under fully-plastic conditions. The generality of the model is demonstrated by analysing the full elasto-plastic response of a hollow sphere and discussing the implications of the computational results.     

Elastic-viscoplastic analysis of plates by the finite element method

In this paper the finite element technique is employed in the solution of elastic-viscoplastic plate bending problems. The method is applicable to both thick and thin plates and by attaining steady-state conditions the process offers an alternative method of solution for static elasto-plastic situations. A quadratic isoparametric element based on Mindlin plate theory is adopted and the Euler time-stepping scheme is employed in solution. Yield criteria are based on moment resultants and the Von Mises, Tresca and Johansen forms are included. Several numerical examples are presented and the results compared with those from other sources where available     

Numerical procedure for the deflections of buckled elasto-plastic flexible bars

In this paper, a numerical procedure to determine the deflections at the free end and along the central line of buckled elasto-plastic flexible bars is introduced.Because of the large deflection of the bar, the nonlinear theory of bending is used to solve the problem at hand. The exact expression of the curvature is used in the moment-curvature relationship for both the elastic (elastica) and the elasto-plastic states of stress.For the elastica problem, a closed-form solution may be found, if any. However, for elasto-plastic flexible bars, where a region of the bar yields, and yielding progresses along the bar, a closed-form solution is not possible because of the complexity of the problem.Therefore, the resulting first-order, nonlinear differential equations, for the problem at hand, are numerically integrated, using the improved Euler method, from the base of the bar where boundary values are known, to the free end where boundary value must initially be guessed. The integration process is repeated until the computed value of deflection at the free end of the bar is close enough to the trial value within acceptable tolerance. Deflections at the free end of the bar in the x and y directions are presented in graphical form. A computer program is developed, and the results are compared to those obtained from the experimental data.     

Optimization of inelastic annular plates with cracks

Stepped plates made of a fibre-reinforced composite material are studied. The plates are subjected to the initial impulsive loading, which imparts the plates given kinetic energy. Optimal designs corresponding to the minimum of the maximal residual deflections are established making use of the variational methods of the theory of optimal control. Maximal deflections are evaluated with the method of mode form motions.     

Deflection and stress analysis of orthotropic plates in flexure

A finite difference (FD) method is developed for computing deflections and stresses in rectangular orthotropic plates subjected to transverse flexural loadings. The plate material is elastic with symmetry axes parallel to the plate edges, and plate deflections are assumed to be small. The FD equations are solved iteratively using successive over relaxation techniques. The numerical procedure converges rapidly and is simple enough to be implemented in a minicomputer program for the design analysis of composite plates. As an example the program is applied to the analysis of simply supported and clamped square plates under uniform pressure or point loads, and the effect of material anisotropy on plate behaviour is discussed.     

Dynamic response of plate to moving loads: Structural impedance method

An algorithm based on a structural impedance approach has been developed to study the transient response of plates with arbitrary boundary conditions and subjected to moving loads. Thin plate theory is assumed for the plate model and the algorithm places no restrictions on the loading conditions. The algorithm accounts for the complete dynamic interactions between the moving loads and the plate. Therefore, the method can be applied to the general moving mass problems and to the simplified moving force and static problems. The accuracy of the algorithm is verified by comparing the results obtained from the structural impedance method (SIM), in the case of moving force solutions, with the available exact solutions and with other numerical results. The dynamic deflections obtained from the moving mass solutions are compared with available experimental results. Parametric analyses over a wide spectrum of velocities and mass ratios indicate that the inertial effect on dynamic deflections is pronounced when the vehicle is traveling at high speed.     

Post-buckling behaviour of elastic circular plates using a simple finite element formulation

The post-buckling behaviour of elastic circular plates is studied in this paper using a simple finite element formulation. The final linearized eigenvalue problem is solved by using three numerical methods and all these methods are found to yield accurate results for moderately large deflections. Comparison of the present results with the results existing in literature shows the validity of this formulation.     

Large Deflection Analysis of a Thin Plate: Computer Simulations and Experiments

Many previous studies have conducted computer-aided simulations ofelastic bodies undergoing large deflections and deformations, but therehave not been many attempts to validate their numerical results. Thesubject of this paper is a thin clamped plate undergone large vibrationdue to attached end-point weight. The main aim of this paper is to showthe validity of the absolute nodal coordinate formulation (ANCF) bycomparing to the real experiments. Large oscillations of thin plates arestudied in the paper with taking into account effects of an attachedend-point weight and aerodynamic damping forces. The physicalexperiments are carried out using a high-speed camera and dataacquisition system. For numerical modeling of the plate, the absolutenodal coordinate formulation is used.     

Application of the initial value method to analysis of elastic-plastic plates and shells of revolution

Basic idea of a modification of initial value methods is shown and its application to computation of elastic-plastic shells and plates of revolution is presented.

Analysis of large deflections of spherical caps made of material with isotropic and/or kinematic strain-hardening is carried out. Limit points for external pressure are computed for full-walled and equivalent ideal sandwich cross-sections.

Perturbating the membrane state the bifurcation loads of Shanley's either Karman's type are computed for annular plates under uniform radial compression. Limit points are also computed for different boundary conditions.

Analysis of spherical caps subject to changes of temperature and pressure is presented. For load control programs determined in the plane load parameters (pressure and temperature) neutral domain curves of elastic unloadings are evaluated.