Nonlinear finite element for modeling reinforced concrete columns in three-dimensional dynamic analysis

A new finite element is proposed for slender, flexure-dominated reinforced concrete columns subjected to cyclic biaxial bending with axial load, and its implementation into a program for the nonlinear static or dynamic analysis of structures in three-dimensions, is described. The element belongs to the class of distributed inelasticity discrete models for the nonlinear dynamic response analysis of frame structures to earthquake ground motions. The element tangent flexibility matrix is constructed at each time step by Gauss-Lobatto integration of the section tangent flexibility matrix along the member length. The tangent flexibility matrix of the cross-section relates the increment of the vector of the three normal stress resultants N, M_y, M_z, to the vector increment of the section deformation measures. ε_o, _y, _z, and is constructed on the basis of the bounding surface of the cross-section, which is defined as the locus of points in the space of the normalized N, M_y, M_z, which correspond to ultimate strength. The bounding surface concept enables the model to produce realistic predictions for the nonlinear response of the cross-section to any arbitrary loading path in the space N-M_y-M_z.The bounding surface is introduced and utilized in a very flexible manner, enabling a variety of cross-sectional shapes to be treated in a unified way. As this flexibility is at the expense of computational simplicity and memory size requirements, emphasis is placed on algorithmic techniques to facilitate numerical implementation and to increase computational efficiency.     

Nonlinear three-dimensional resonance analysis of shells

This study details geometrically and physically nonlinear analysis of thin shells in resonance regions of vibration. Generalized analysis of motion with implementation of the FETM-method and of updated Lagrangian formulation is also studied. Utilization of the multigrid spatial simulation mesh for geometric representation of the shell as well as of the anisotropy of material is put forth. Special numerical techniques for solving nonlinear resonance equations of motion are presented. Illustrative numerical solutions of nonlinear resonance response of thin shell structures are performed.     

Nonlinear dynamic analysis of piezoelectric-bonded FG-CNTR composite structures using an improved FSDT theory

Engineering with Computers - In the present work, a geometrically nonlinear finite shell element is first presented to predict nonlinear dynamic behavior of piezolaminated functionally graded...     

Nonlinear dynamic analysis of space trusses

A computational procedure is presented for predicting the dynamic response of space trusses with both geometric and material nonlinearities. A mixed formulation is used with the fundamental unknowns consisting of member forces, nodal velocities and nodal displacements. The governing equations consist of a mixed system of algebraic and differential equations. The temporal integration of the differential equations is performed by using an explicit half-station leap-frog method. The advantages of the proposed computational procedure over explicit methods used with the displacement formulation are discussed. The high accuracy of the procedure is demonstrated by means of numerical examples of plane and space trusses. The constitutive relations in these examples are assumed, for convenience, to be represented by the Ramberg-Osgood polynomials. Comparison is also made with solutions obtained by using implicit multistep temporal integration schemes.     

Nonlinear dynamic analysis of stiffened plates

A new finite strip formulation for the nonlinear analysis of stiffened plate structures subjected to transient pressure loadings is presented. The effects of large deflections, and strain rate sensitive yielding material properties are included. An explicit central difference/diagonal mass matrix time stepping method is adopted. Example results are presented for an I-beam, an isotropic plate and a five-bay stiffened panel and compared with other predictions and/or experimental results. It is observed that design level accuracy can be obtained for practical structures for a fraction of the cost of full finite element analyses.     

Nonlinear dynamic analysis of curved beams

A computational procedure is presented for predicting the dynamic response of curved beams with geometric nonlinearities. A mixed formulation is used with the fundamental unknowns consisting of stress resultants, generalized displacements and velocity components. The governing semidiscrete finite element equations consist of a mixed system of algebraic and differential equations. The temporal integration of the differential equations is performed by using an explicit half-station central difference method. A procedure is outlined for lumping both the flexibilities and masses of the mixed model, thereby uncoupling all the equations of the system. The advantages of the proposed computational procedure over explicit methods used with the displacement formulation are discussed. The effectiveness and versatility of the proposed approach are demonstrated by means of numerical examples.     

A general three-dimensional L-section beam finite element for elastoplastic large deformation analysis

In this paper, the development of a general three-dimensional L-section beam finite element for elastoplastic large deformation analysis is presented. We propose the generalized interpolation scheme for the isoparametric formulation of three-dimensional beam finite elements and the numerical procedure is developed for elastoplastic large deformation analysis. The formulation is general and effective for other thin-walled section beam finite elements. To show the validity of the formulation proposed, a 2-node three-dimensional L-section beam finite element is implemented in an analysis code. As numerical examples, we first perform elastic small and large deformation analyses of a cantilever beam structure subjected to various tip loadings, and elastoplastic large deformation analysis of the same structure under reversed cyclic tip loading. We then analyze the failures of simply supported beam structures of different lengths and slenderness ratios under elastoplastic large deformation. The same problems are solved using refined shell finite element models of the structures. The numerical results of the L-section beam finite element developed here are compared with the solutions obtained using shell finite element analyses. We also discuss the numerical solutions in detail.     

Nonlinear dynamic structural analysis using dynamic relaxation with zero damping

The main idea of the paper is to present a dynamic relaxation algorithm that does not require the damping matrix and velocity terms. The general formulation suggested in this article covers the common DRM as well. In order to verify the ability of the new technique, the obtained static and dynamic solutions are checked with the ones found by the other scheme. When the loads are variable and the behavior of the system is extremely nonlinear, the proposed procedure works efficiently.     

A co-rotational formulation for nonlinear dynamic analysis of curved euler beam

A co-rotational finite element formulation for the dynamic analysis of a planar curved Euler beam is presented. The Euler-Bernoulli hypothesis and the initial curvature are properly considered for the kinematics of a curved beam. Both the deformational nodal forces and the inertial nodal forces of the beam element are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory in element coordinates which are constructed at the current configuration of the corresponding beam element. An incremental-iterative method based on the Newmark direct integration method and the Newton-Raphson method is employed here for the solution of the nonlinear dynamic equilibrium equations. Numerical examples are presented to demonstrate the effectiveness of the proposed element and to investigate the effect of the initial curvature on the dynamic response of the curved beam structures.     

Nonlinear and dynamic structural analysis using combined approximations

It is shown how the combined approximations (CA) approach, developed originally for linear reanalysis, can improve the solution efficiency of nonlinear and dynamic analysis problems. In such problems the analysis equations are modified repeatedly during the solution process. The CA approach is based on the integration of several concepts and methods. The advantage is that efficient local approximations and accurate global approximations are combined to achieve an effective solution procedure. Some numerical examples demonstrate how the CA method can be used as a general tool in various structural analysis problems.     

Use of three-dimensional dynamic analysis to interpret earthquake damage

A comparison is made for several major items of electrical equipment between observed behavior and response predicted using a general three-dimensional dynamic analysis. This was done as part of a major study for the Bonneville Power Administration. The items of equipment were subjected to ground motions from the 9 February 1971, San Fernando Earthquake which resulted in major damage. The correlation between analyses and observed behavior provided a general verification of the analysis procedures used.     

Nonlinear pattern theory

Summary The formal treatment of patterns is extended to include the nonlinear patterns ABORT and FENCE and their derivatives. Many results for linear patterns carry over to the nonlinear case and several new results are derived. The theory is applied to analyzing the behavior of a class of patterns to parse programming languages operating in back-up-free fashion. The development leads to considerations of the validity of certain forms of recursive pattern definition. Implications to the recognition of recursively-defined Formal Languages are discussed.     

Nonlinear finite element analysis of shells: Part I. three-dimensional shells

A nonlinear finite element formulation is presented for the three-dimensional quasistatic analysis of shells which accounts for large strain and rotation effects, and accommodates a fairly general class of nonlinear, finite-deformation constitutive equations. Several features of the developments are noteworthy, namely: the extension of the selective integration procedure to the general nonlinear case which, in particular, facilitates the development of a ‘heterosis-type’ nonlinear shell element; the presentation of a nonlinear constitutive algorithm which is ‘incrementally objective’ for large rotation increments, and maintains the zero normal-stress condition in the rotating stress coordinate system; and a simple treatment of finite-rotational nodal degrees-of-freedom which precludes the appearance of zero-energy in-plane rotational modes. Numerical results indicate the good behavior of the elements studied.     

Nonlinear generalised dynamic inversion for aircraft manoeuvring control

The nonlinear control problem of aircraft trajectory tracking is tackled in the framework of multiple linear time-varying constrained control using the newly developed paradigm of generalised dynamic inversion. The time differential forms of the multiple constraints encapsulate the control objectives, and are inverted to obtain the reference trajectory-realising control law. The inversion process utilises the Moore–Penrose generalised inverse and the associated nullspace projection, and it predictably involves the problematic generalised inversion singularity. Thus, a singularity avoidance scheme based on a new type of dynamically scaled generalised inverses is introduced that guarantees both asymptotically stable tracking and singularity avoidance. The steady-state closed-loop system allows for two inherently noninterfering control actions working towards a unified goal to exploit the aircraft's control authority over the entire state space. One control action is performed by the particular part of the control law on the range space of the transposed constraint matrix, and it works to impose the prescribed aircraft constrained dynamics. The other control action is performed by the auxiliary part of the control law on the complementary orthogonal nullspace of the constraint matrix, and it provides aircraft's global inner stability using the concept of perturbed feedback linearisation. Numerical simulations of an aggressive multiaxial aircraft coordinated manoeuvre verify the efficacy of designing nonlinear flight control systems via this methodology.