Tetsuya Yao

The plastic node method: A new method of plastic analysis

In 1968, Ueda and his colleagues developed the new mechanism of plastic hinge based on the incremental theory of plasticity and derived the elastic-plastic and plastic stiffness matrices for one-dimensional members. Using this plastic hinge, a method of elastic-plastic analysis of space-framed structures was well developed including the effect of large deflection. n nIn this paper, extending the basic idea of this plastic hinge method, a new method for plastic analysis of plates and solid bodies is developed. The basic theory of the new method is presented using the ordinary finite element method (the stiffness method). n nIn this theory, the yield condition at the ith node of an element is described as follows: “The ith node becomes plastic when the resultant stresses at this node satisfy the appropriate plasticity condition and the plastic deformation is developed only at the nodes”. In this sense, the authors named this method the ‘Plastic Node Method’. n nFor the element with k plastic nodes, the relation between the increments of the nodal force, dx, and the nodal displacement, du, is derived in the following form: dx = Kpdu. Kp in this equation is either elastic-plastic or plastic stiffness matrix and is expressed in explicit form. n nWhen an element is subjected to constant strain, the element becomes plastic in the entire volume if the yield condition is satisfied at any point. Simultaneously, the plastic node is formed at every node of the element. Completely the same plastic stiffness matrix is obtained by either the ordinary finite element method or the present plastic node method. A similar fact is observed when a plate element is subjected to uniform bending. From these facts the accuracy of the solution by this method is anticipated to be the same order as that by the ordinary finite element method when the element division increases. n nThe plastic node method is quite general for plastic analysis since this can be applied to a continuum of any geometrical shape, and example analyses by this method demonstrate the validity and usefulness of the method.

Ultimate strength of compressed stiffened plates and minimum stiffness ratio of their stiffeners

A theoretical investigation into the effectiveness of a stiffener against the ultimate strength of a stiffened plate is carried out. Series of the buckling analyses, the elastic large deflection analyses and the elastic-plastic large deflection analyses are performed by the analytical method and the finite element method on the stiffened plate under thrust. Experiments are also carried out on the stiffened plate under thrust to confirm the theoretical results. n nOn buckling of a stiffened plate, it is well known that ther exxists a minimum stiffness ratio of a stiffener to the plate, λBmin, which gives the maximum limiting value of the buckling strength. Concerning the ultimate strength it was confirmed that there exists a significant stiffness ratio of a st stiffener to the plate, λUmin similar to λBmin for the buckling strength. n nIt was also found that there are three typical collapse modes for the stiffened plate under thrust, that is: (1) MODE OO, overall collapse after overall buckling; (2) MODE LO, overall collapse after local buckling; (3) MODE LL, local collapse after local buckling. n nApproximatelmethods are proposed to evaluate the ultimate strength and λUmin of a multi-stiffened plate under thrust. n nThe effects of initial imperfections such as welding residual stresses and initial deflection on ultimate strength and λUmin of a stiffened plate under thrust are also discussed.

Brittle Fracture Initiation Characteristics under Bi-axial Loading

In this paper, brittle fracture initiation characteristics of plate with an inclined crack which is subjected to bi-axial tensile load is investigated by using cruciform specimens made of polymethylmethacrylate (PMMA) which is perfectly brittle material, and mild steel which is accompanied with small scale yielding. The brittle fracture tests of the cruciform specimen under proportional loading ratio of 1/ 2, 1/1 and 0/1, and the non-cruciform or straight edge specimen under uni-axial loading for comparison are conducted.The test results on direction of fracture initiation and load at fracture are analyzed by applying the following concepts : (1) maximum tangential stress, σθ, max (2) minimum strain energy density factor, Smin (3) maximum decreasing rate of total potential energy, Gθ, max.The test results can be explained fairly in terms of σθ, max in which a certain ambiguity remains. The experimental values except the case of direction of fracture initiation for load ratio 1/2 agree with the calculated ones by Smin concept. However, the physical meaning of Smin is not understandable. Gθ, max concept is based on the Griffith-Orowan energy condition. Practically, Gθ, max is evaluated by finite element method instead of analytical method. Therefore, the experimental results can be explained most clearly by applying Gθ, max concept.Test results lead to the following conclusions :(1) Gθ, max concept is the most suitable one in discussing the brittle fracture behaviors under mixed mode condition. The mixed mode means the combination of tensile and in-plane shear ones.(2) In case of load ratio 1/2, as the inclined angle of the notch to the direction of the main load, β, decreases, the load at fracture increases at maximum up to 2. 4 times as that for β=90°.(3) In case of load ratio 1/1, that is, equi-axial load, the load at fracture does not vary with β, and the direction of fracture initiation coincides with the line of notch.(4) In case of load ratio 0/1, that is, uni-axial load, the load at fracture increases as β decreases. However, the direction of fracture initiation is almost normal to the load irrespective of β.

Buckling/Plastic Collapse Behavior and Strength of Plate Girders Subjected to Combined Bending and Shear Loads

This chapter deals with buckling/plastic collapse behavior and the ultimate strength of plate girders subjected to shear and bending loads as well as their combinations. More than 50 years ago Busler and Fujii conducted research works related to this issue including a series of experiments. The fundamental findings related to this issue is briefly introduced at the beginning.

Progressive Collapse Behavior and Ultimate Strength of Hull Girder of Ship and Ship-Like Floating Structures in Longitudinal Bending

This chapter deals with the most important strength of ship structure: the ultimate longitudinal strength. At the beginning, early research works are reviewed related to the ultimate hull girder strength including strength tests using existing ships. Then, the progressive collapse of hull girder in bending is briefly explained in relation to the development of calculation method.

Fundamental Theory and Methods of Analysis to Simulate Buckling/Plastic Collapse Behavior

This chapter deals with the fundamental theory and method for the analysis of buckling/plastic collapse behavior of rectangular plates and stiffened plates subjected to combined in-plane loads. First, based on the fundamentals in the bucking collapse behavior of plates and stiffened plate under various loading conditions, the deflection modes that should be used for the analytical method of elastic buckling and postbuckling analyses are explained. Then, the fundamental theories for the elastic buckling analysis and elastic large deflection analysis are presented including how to consider the effect of initial imperfections such as initial deflection and welding residual stresses. For the buckling/plastic collapse analysis of plates and stiffened plates considering both geometrical and material nonlinearities, the numerical approach such as the finite element method needs to be used. The fundamental theory for the elastoplastic large deflection analysis is explained taking a four-node isoparametric shell element as an example. These theory and methods are used for the analytical and numerical calculations in the continued chapters in this book.

Buckling/Plastic Collapse Behavior of Structural Members and Systems in Ship and Ship-Like Floating Structures

This chapter deals with buckling/plastic collapse behavior and the ultimate strength of structural members and systems, some of which are not the main structural members.

Chapter 4 – Buckling/Plastic Collapse Behavior and Strength of Rectangular Plate Subjected to Uni-Axial Thrust

This chapter deals with buckling/plastic collapse behavior and the ultimate strength of rectangular plate subjected to uni-axial thrust. At the beginning, elastic buckling and postbuckling behavior are explained as fundamentals. Then, elastic behavior is explained including buckling and postbuckling behavior including secondary buckling. Regarding buckling, influences of boundary condition and welding residual stress on buckling strength are explained and so the influence of plate-stiffener interaction on buckling strength in the case of stiffened plate. Secondary buckling is also explained in the case of short plate and long plate.

Theoretical Background and Assessment of Existing Design Formulas to Evaluate Ultimate Strength

There exist some formulas to evaluate the ultimate strength of stiffened plates specified in common structural rules (CSRs). Some of them have theoretical background but some of them no background. This chapter deals with such rule formulas.

Initial Imperfections due to Welding

Ship and ship-like floating structures are constructed by welding and the structural members and systems are accompanied by initial imperfections such as welding residual stress and initial deflection/distortion produced by welding. In general, such initial imperfections affect the strength and the stiffness of structural members and systems. From this viewpoint, it is very important to understand what initial imperfections are produced.