Dynamic Elastic-plastic Analysis Research Articles

Dynamic Analysis Of Prestressed Concrete BeamsUnder Impact And High Speed Loadings

An elastic-plastic dynamic analysis method based on the beam elements is developed in order to investigate the dynamic behavior of PC beams under impact loading. First, the limit dropping height in the impact test is predicted by the high speed loading analysis. Second, the impact test is performed in order to confirm the failure behavior of the bonded and unbonded PC beams by using the newly built weight dropping machine. Finally, the impact failure analysis is developed in order to simulate the results obtained by the impact test.

Dynamic elastic-plastic analysis by a symmetric Galerkin boundary element method with time-independent kernels

Boundary integral equations formulated by the combined use of single-layer and double-layer sources in such a way that the integral operator is symmetric (with respect to a suitable bilinear form), and their discretization by a Galerkin weighted-residual procedure are the basic features of the ‘symmetric Galerkin boundary element method’ (SGBEM). This approach, which has been applied to various mechanical problems in the last few years, is proposed and developed herein for elastic-plastic dynamic analysis using elastostatic kernels (i.e. time independent Green functions for unbounded spaces) for displacements and tractions on the boundary and for stresses and displacements on the domain. Thus only double integrations are required (instead of quadruple required by elastodynamic kernels) at the price of domain integrals. Regularization procedures for singular integrals are developed. Assuming material behaviours as elastic-plastic stable (in Drucker sense) and suitable multifield modelling in space, basic results for a computational theory are established (extremum property and uniqueness of time-step solution, convergence of an iterative solution algorithm, algorithmic stability along the step sequence). Finally, the SGBEM developed is corroborated by two numerical comparative tests.

An Iterative Approach to Dynamic Elastic-Plastic Analysis

The step-by-step analysis of structures constituted by elastic-plastic finite elements, subjected to an assigned loading history, is here considered. The structure may possess dynamic and/or not dynamic degrees-of-freedom. As it is well-known, at each step of analysis the solution of a linear complementarity problem is required. An iterative method devoted to solving the relevant linear complementarity problem is presented. It is based on the recursive solution of a linear complementarity, problem in which the constraint matrix is block-diagonal and deduced from the matrix of the original linear complementarity problem. The convergence of the procedure is also proved. Some particular cases are examined. Several numerical applications conclude the paper.

An Approximate Technique for Dynamic Elastic-Plastic Analysis

The possibility of obtaining an approximate sufficiently reliable response for elasticplastic discretized structures subjected to dynamic load (kinematical and/or mechanical), with alow computational effort, has been considered. A suitable technique to this effect comes from the form of the dynamic influence matrix of imposed plastic strains on self-stresses, which is shaped by adding up a sparse time-dependent matrix and a block diagonal time-independent matrix (which is the sum of two block diagonal matrices). Several cases of practical interest have been studied, among these cases a special one where all the degrees-of-freedom are dynamic. The technique is compared to other approximate techniques. The structures the elements of which have monodimensional elastic domain are considered with special attention.

Dynamic plasticity analysis by boundary/interior elements

A symmetric/sign-definite BEM formulation is employed to address the dynamic elastic-plastic analysis problem. Two space discretizations are operated, one based on the Hu-Washizu principle with boundary elements, the other based on the maximum plastic work theorem of plasticity theory with interior elements. The original continuum problem can in this way be transformed into a BE/IE discretized one, governed by a system of Volterra time-integral equations of first kind coupled with a set of discrete complementarity conditions which enforce plasticity laws at the interior plastic nodes. A subsequent time discretization generates a sequence of step problems, each of which is characterized by a variational principle of deformation-theory plasticity. A solution procedure is discussed, but no numerical results are presented.

上下地震動を受ける二層立体ラチスドームの耐震性に関する研究

The present study is concerned with the earthquake resistant capacity of the double layer latticed dome due to vertical motions by elastic-plastic dynamic analysis, considering both of geometric and material non-linearities. The earthquake resistant capacity is evaluated by the max-imum acceleration of the input wave which induces dynamic collapse of the dome. As the results of this study, (i) the configuration of dynamic collapse is observed that the central part of the dome deforms downward larger than the peripheral part by occurence of chain buckling of the several members, and (ii) an approximate method for estimating the collapse acceleration of the latticed dome has been proposed and the validity has been shown.

A large deformation elastic-plastic dynamic analysis of square plate and spherical shell subjected to shock loadings

Based on Bathe's methodology and Yuan's formulation, a large deformation elastic-plastic transient dynamic finite element method is proposed for shock loading dynamic analysis on simple local structure, such as square plate and spherical shell. The verification of the adopted method shows good agreement with related literature. The proposed method is then extended to study strong shock loading problems on local structure. The displacement/acceleration time histories with plastic zone spread phenomenas are shown in several interesting figures.

Elastic-plastic dynamic analysis of anisotropic laminated plates

This paper presents the application of a refined finite element model to the elastic and elastic-plastic dynamic analysis of anisotropic laminated plates. Dynamic analysis is based on Newmark's algorithm used in conjunction with the Hughes and Liu predictor-corrector scheme resulting in an ‘ effective static problem’ which is solved using a Newton-Raphson-type process. Flow theory is used in the inelastic range and the Huber-Mises yielding surface extended by Hill for anisotropic materials is adopted. Numerical results obtained for two categories of anisotropic structures, namely cross-ply laminated plates and angle-ply laminated plates, are presented and the effects of anisotropy and bending/ stretching coupling on the dynamic elastic and elastic-plastic responses are discussed. The effects of lamina stack sequences and lamina angle sequences on the dynamic responses are also considered.

Elastic-plastic analysis of a dynamically loaded circumferentially notched round bar

Dynamic elastic-plastic finite-element analyses of a circumferentially notched round bar subject to loading by a tensile stress pulse are presented. The finite-element study is motivated by the dynamic fracture initiation experiment introduced by Costin, Duffy and Freund and therefore provides a critique of this experiment. Static elastic-plastic analyses are carried out for externally notched round bars of various relative crack depths. The J integral is calculated at each load increment using an invariant finite-domain integral representation for the energy release rate. These values of J, obtained by integrating the computed field quantities over arbitrary contours and areas enclosed by the contours, are taken as the reference values. Through comparison with these results, we evaluate the accuracy of a deep crack formula based on the load-displacement behavior. Similar formulas are frequently employed for fracture toughness measurements using standardized test configurations. In the dynamic elastic-plastic analysis, the circumferentially notched round bar subject to a tensile pulse is examined. A uniform rate of loading is applied at one end of the bar to simulate the long pulse loading in the experiment. An invariant finite-domain integral expression, which is particularly suited for finite-element analyses, is employed to calculate the dynamic energy release rate. Our analyses provide some insight concerning the accuracy of these invariant domain integral expressions and their usefulness in computational studies. We also calculate the value of the J integral from the load-displacement behavior, using a formula proposed by Costin, Duffy and Freund. The present study clarifies the applicability of such a formula for the determination of the dynamic fracture toughness and provides information concerning the effect of relative crack depth and the extent of plasticity on its accuracy.

Dynamic Tests of Cracked Pipe Components

Dynamic tests were conducted involving notched sections of 4-in. (10-cm) stainless steel and Inconel-600 pipe. The specimen was a four-point bending beam with end masses sized to give an elastic first-mode frequency near that of typical field-installed piping systems (15 Hz). Specimens were loaded using sinewave excitation at this first mode natural frequency. Specimen response was compared to predictions from an elastic-plastic dynamic analysis previously developed on this program. In addition, specimen loads at failure were compared to those predicted from a net section collapse failure criterion. The results confirmed that the elastic-plastic dynamic analysis adequately predicted the dynamic response of flawed pipes under seismic-type excitation. Furthermore, net section collapse does not occur under dynamic loading conditions which simulate natural frequencies of as-installed light water reactor piping systems. Finally, a net section collapse criterion yields conservative estimates of the load capacity of flawed pipe sections provided crack growth is properly accounted for.

Dynamic Elastic-Plastic Behavior of Circumferential Cracks in a Pipe Subject to Seismic Loading Conditions

An analytical study is performed to investigate the structural stability, and inherent integrity, of a Pressurized Water Reactor primary coolant loop cold leg pipe containing a through-wall circumferential crack. The purpose of this study is to gain a better understanding of the mechanisms and extent of crack opening behavior in a real piping system, and, thus, establish the basis for improved pipe break criteria. Cracks extending one-half the circumference or greater are considered in the pipe. Combined operating pressure plus external seismic loads are applied simultaneously to cause a maximum crack opening effect. A dynamic elastic-plastic analysis is performed to calculate stress intensity factors at the crack tip. The results are compared with experimental fracture toughness data to assess the material’s capability to resist crack extension. A fatigue crack growth study is also performed to determine the range of initial flaw sizes which could grow and extend during normal operation to threaten the integrity of the cold leg pipe.

On finite element large displacement and elastic-plastic dynamic analysis of shell structures

Finite element procedures for nonlinear dynamic analysis of shell structures are presented and assessed. Geometric and material nonlinear conditions are considered. Some results are presented that demonstrate current applicabilities of finite element procedures to the nonlinear dynamic analysis of two-dimensional shell problems. The nonlinear response of a shallow cap, an impulsively loaded cylindrical shell and a complete spherical shell is predicted. In the analyses the effects of various finite element modeling characteristics are investigated. Finally, solutions of the static and dynamic large displacement elastic-plastic analysis of a complete spherical shell subjected to external pressure are reported. The effect of initial imperfections on the static and dynamic buckling behavior of this shell is presented and discussed.

Cyclic elastic-plastic dynamic analysis by the finite element method

A finite element approach for cyclic elastic-plastic dynamic analysis is presented. A hardening model suited for cyclic plasticity behavior is incorporated. It is composed of several yield surfaces, and nonlinear stress-strain curves can be included. The central difference timewise operator is employed to solve the equations of motion. Comparison is made with the Newmark operator. Numerical examples illustrate the effect of cyclic plastic deformations on the dynamic response of simple problems. Comparison is presented for the structural behavior as predicted by the present hardening model and by the isotropic hardening model.

Elastic-plastic dynamic analysis of axisymmetric solids

This paper presents an application of isoparametric elements for the elastic-plastic dynamic analysis of shells of revolution. General isoparametric elements with curved sides are used in the finiic element discretization. These are capable of representing solids of revolution in the form of a layered system. Structures with complex geometries and sharp discontinuities may be studied. Solutions can be obtained for both thin and thick shells because the customary Kirchhoff-Love hypothesis is not invoked. Dynamic analysis is carried out by means of step-by-step integration, the program allowing for the use of any of the schemes belonging to the Newmark family of methods (with free parameters γ and β) and the Wilson and Farhoomand θ-method. Flow theory of plasticity is used in the inelastic range and either isotropic hardening or kinematic linear hardening may be adopted. The program can analyze axisymmetric structures subjected To axially symmetric loading as well as plane stress problems. Numerical examples presented include the dynamic analyses of a simply supported beam and two spherical caps.

Discussion of “Dynamic Elastic-Plastic Analysis of Structures”

Discussion of “Dynamic Elastic-Plastic Analysis of Structures”

Dynamic Elastic-Plastic Analysis of Structures

Finite difference method is presented; design of structure to with-stand h-p loadings of transient or time dependent nature such as nuclear blasts, requires abandoning conventional requirement of limiting stresses to some value below elastic limit; plastic flow at various locations in structure is permitted, but total deflection must be kept within acceptable limits.

Closure to “Dynamic Elastic-Plastic Analysis of Structures”

Closure to “Dynamic Elastic-Plastic Analysis of Structures”

Discussion of “Dynamic Elastic-Plastic Analysis of Structures”

Discussion of “Dynamic Elastic-Plastic Analysis of Structures”

Dynamic Elastic-Plastic Analysis of Structures

Finite difference method is presented; design of structure to with-stand h-p loadings of transient or time dependent nature such as nuclear blasts, requires abandoning conventional requirement of limiting stresses to some value below elastic limit; plastic flow at various locations in structure is permitted, but total deflection must be kept within acceptable limits.