Wen-I Liao

AN UNCONDITIONALLY STABLE EXPLICIT METHOD FOR STRUCTURAL DYNAMICS

An explicit integration method with unconditional stability was proposed and presented in this paper. Numerical characteristics of this explicit method for linear elastic sys-tems are almost the same as those of the constant average acceleration method while for a nonlinear system it is more efficient in computing than for the constant average acceleration method. This explicit method integrates the most promising advantages possessed by the explicit and implicit methods. No limitation on the time step in satisfying the stability limit, which is the most important property for an implicit method, is theoretically proved for this explicit method. Furthermore, the avoidance of solving any implicit system or using any iterative procedure, which usually brings considerable simplification in practical applications for explicit methods, leads to the very low cost of one explicit step. Thus, the computational effort can be significantly reduced when compared to implicit methods in each time step. Consequently, this explicit method can be used to solve dynamic problems efficiently due to the unconditional stability and the very low cost of explicit steps. Rough guidelines with regards to the selection of a time step in achieving accurate solutions for the constant average acceleration method are also appropriate for the proposed explicit method.

Dynamic responses of bridges subjected to near-fault ground motions

Abstract The motivation of this paper is to study the dynamic behavior of bridge structural systems subjected to both near‐fault and far‐field ground motions. A highway bridge containing a hinge supported continuous girder with six concrete piers was selected for this study. The Chi‐Chi (Taiwan) earthquake was selected as a first set in this study to provide the near‐fault earthquake characteristics. On the other hand, another earthquake record was selected to illustrate far‐field earthquake characteristics for comparison. The results show that near‐fault earthquake ground motions cause more ductility demands and base shear than far‐field earthquake ground motions.

Preliminary study on the fragility curves for highway bridges in Taiwan

Abstract This paper describes procedures of bridge fragility analysis for the highway bridges on the south‐north freeway in Taiwan, and studies the evaluation of parameters used in bridge damage assessment. The fragility curves are used to represent the probabilities that structural damage, under various levels of seismic excitation, exceed specified damage states. Since it is neither necessary nor practical to evaluate individual bridges, bridge classification and mapping scheme plays an important role. Calculation of site‐specific seismic demand and damage functions (i.e., capacity curves and fragility curves) are the key features in bridge damage assessment and earthquake loss estimation.

On Evaluation of Lamb's Integrals for Waves in a Two-Dimension Elastic Half-Space

In this paper, a modified version of the method of steepest descent is proposed for the evaluation of Lambs integrals which can be considered as basis functions dealing with the development of the transition matrix method which can be used to study the wave scattering in a two-dimensional elastic half-space. The formal solutions of the generalized Lambs problem are studied and evaluated on the basis of the proposed method. After defining a phase function which presents in wavenumber integral, an exact mapping and an inverse mapping can be obtained according to the phase function. Thus, the original integration path can be deformed into an equivalent admissible path, namely, steepest descent path which passed through the saddle point, and then mapped onto a real axis of mapping plane, finally, resulted in an integral of Hermite type. This integral can be efficiently evaluated numerically in spite of either near- to far-field or low to high frequency. At the same time, the asymptotic value can easily be obtained by applying the proposed method. The numerical results for generalized Lambs solutions are calculated and compared with analytic, asymptotic or other existing data, the excellent agreements are found. The properties of generalized Lambs solutions are studied and discussed in details. Their possible applications for wave scattering in elastic half-space are also pointed out.

Cyclic Performance of Two-Story Ductile RC Frames With Infill Walls

This paper presents the results of the experimental and analytical investigations conducted on four 0.8 scale 2-story one bay ductile reinforced concrete frames with infill nonstructural walls subjected to cyclically increasing loads. The material properties and the member sizes of beams and columns in the four RC frame specimens are identical, but with different types of infill nonstructural wall. These four frames are the pure frame, frame with short column, frame with short beam and frame with wing walls. The four RC frame specimens were designed and constructed according to the general prototype building structures in Taiwan. Test results indicate that the ductility behavior of the frames with infill wall is similar to those of the pure frame. The ultimate base shear strength of the frames with infill walls is higher than those of the pure frame. Analytical results show that the proposed simplified multi-linear beam-column element implemented in a general purpose structural analysis program can accurately simulate the cyclic responses of the RC frame specimen incorporating the elastic flexural stiffness computations suggested by the model building codes.Copyright

The transition matrix for the scattering of elastic waves in a half‐space

Abstract In this paper, the transition matrix for elastic waves scattering from an alluvium on an elastic half‐space is developed. Bettis third identity is employed to establish orthogonality conditions among basis functions that are Lambs singular wave functions. The total displacements and associated tractions for both the surrounding half‐space and alluvium are expanded in a Rayleigh series. After the boundary conditions are applied, the T‐matrix can be obtained. Explicit forms of the basis functions are derived for the two‐dimensional anti‐plane and in‐plane problems. The linear transformation is utilized to construct a set of orthogonal basis functions. The transformed T‐matrix is related to the scattering matrix and it is shown that the scattering matrix is symmetric and unitary and that the T‐matrix is also symmetric. Some typical scattering cases induced by incident plane waves are illustrated for verification.

Sensitivity study of gamma‐function pseudodynamic algorithm

Abstract The γ‐function explicit method has been developed for pseudodynamic testing since it can have favorable numerical dissipation. This numerical dissipation originates from the use of the structure‐dependent coefficient matrices in a quadrature equation. These coefficient matrices highly depend upon initial stiffness matrix, which is experimentally determined before the pseudodynamic test. Since the initial stiffness matrix determined from an experimental procedure may be different if a different displacement is imposed upon a specified degree of freedom to obtain its corresponding column, the coefficient matrices will vary accordingly. Sensitivity studies of this variation of the coefficient matrices for numerical properties and error propagation properties are conducted herein. It is revealed by both the analytical and numerical results that the performance of the γ‐function explicit pseudodynamic algorithm for both linear elastic and nonlinear systems is insensitive to the variation of the coefficient matrices in the quadrature equation, especially for a small value of the product of the natural frequency and the size of integration time step.

Dynamic Response of a Hemispherical Foundation Embedded in an Elastic Half-Space

The dynamic response of a massless rigid hemispherical foundation embedded in a uniform homogeneous elastic half-space is considered in this study. The foundation is subjected to external forces, moments, plane harmonic P and SH waves, respectively. The series solutions are constructed by three sequences of Lamb’s singular solutions which satisfy the traction-free conditions on ground surface and radiation conditions at infinity, automatically, and their coefficients are determined by the boundary conditions along the soil-foundation interface in the least square sense. The fictitious eigen-frequencies, which arise in integral equation method, will not appear in the numerical calculation by the proposed method. The impedance functions which characterize the response of the foundation to external harmonic forces and moments at low and intermediate frequencies are calculated and the translational and rocking responses of the foundation when subjected to plane P and SH waves are also presented and discussed in detail.

NUMERICAL DISSIPATION FOR PSEUDODYNAMIC TESTING OF NONLINEAR SYSTEMS

Abstract It is well known that for linear elastic systems favorable numerical dissipation can suppress the spurious growth of high frequency modes while low frequency modes are almost unaffected. Thus, it is interesting to analytically explore the performance of numerical dissipation in the solution of a nonlinear system. In this paper, a novel technique is introduced to evaluate the numerical and error propagation properties of the γ‐function explicit method for nonlinear systems. It is analytically and numerically verified that this method has favorable numerical dissipation not only for linear elastic but also nonlinear systems. In fact, the suppression of high frequency modes for nonlinear systems is analytically proved. The importance of the spectral radius for a nonlinear system is also addressed. The rate of suppression of the spurious growth of high frequency responses will be accelerated due to stiffness hardening while it is decelerated due to stiffness softening.

The Transition Matrix Formalism for the Scattering of an Alluvium on an Elastic Half-Space

This paper develops the transition matrix formalism for scattering from an three-dimensional alluvium on an elastic half-space. Betti’s third identity is employed to establish orthogonality conditions among basis functions that are Lamb’s singular wave functions. The total displacements and associated tractions exterior and interior to the surface are expanded in a Rayleigh series. The boundary conditions are applied and the T-matrix is derived. A linear transformation is utilized to construct a set of orthogonal basis functions. The transformed T-matrix is related to the scattering matrix and it is shown that the scattering matrix is symmetric and unitary and that the T-matrix is symmetric. Typical numerical results obtained by incident plane waves for verification are presented.Copyright