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In this paper, the precise time-step integration method by step-response and impulsive-response matrices is further developed by expanding the dimension of the matrices so as to avoid computing the particular solutions separately. Two new precise time-step integration algorithms with excitations described by second-order and first-order differential equations are proposed. The first method is a direct extension of the existing algorithms. However, the extended system matrices are not symmetrical. In the second method, the Duhamel integrals are used as the particular solutions. As a result, the responses can be expressed in terms of the given initial conditions and the step-response matrix, the impulsive-response matrix and a newly derived Duhamel-response matrix. The symmetry property of the system matrices can be used in the computation. However, it will first require a calculation of the Duhamel-response matrix and its derivative. To reduce the computational effort, the relation between the Duhamel-response matrix and its derivative is established. A special computational procedure for periodic excitation is also discussed. Numerical examples are given to illustrate the present highly efficient algorithms.

The identification of a three dimensional constitutive model is useful for describing the complex mechanical behavior of a nonlinear and anisotropic biological tissue such as the esophagus. The inflation tests at the fixed axial extension of 1, 1.125, and 1.25 were conducted on the muscle and mucosa layer of a porcine esophagus separately and the pressure-radius-axial force was recorded. The experimental data were fitted with the constitutive model to obtain the structure-related parameters, including the collagen amount and fiber orientation. Results showed that a bilinear strain energy function (SEF) with four parameters could fit the inflation data at an individual extension very well while a six-parameter model had to be used to capture the inflation behaviors at all three extensions simultaneously. It was found that the collagen distribution was axial preferred in both layers and the mucosa contained more collagen, which were in agreement with the findings through a pair of uniaxial tensile test in our previous study. The model was expected to be used for the prediction of stress distribution within the esophageal wall under the physiological state and provide some useful information in the clinical studies of the esophageal diseases. [DOI: 10.1115/1.2354206] Keywords: strain energy function (SEF), inflation, constitutive model, collagen

The time-dependent mechanical properties of the porcine esophagus were investigated experimentally and theoretically. It was hypothesized that the viscoelasticity was quasilinear, i.e., the time and strain effects were independent. In order to verify the separability of time and strain effects, the stress-relaxation test was conducted at various strains and the data were fitted with the Fung's quasilinear viscoelastic (QLV) model. By using the material parameters obtained from the stress relaxation test, the cyclic peak stress and hysteresis were predicted. Results showed that the stress relaxed by 20-30% of the peak stress within the first 10 s and stabilized at ~50% at the time of 300 s. The relative stress relaxation [R.sub.2] (i.e., the difference of stress at a particular time to the final equilibrium stress normalized by the total difference of the peak and final stress) was not different significantly for various strains. It was also found that, by using the stress-time data during both the ramp and relaxation phases, the correlation between parameters was substantially reduced. The model could also predict the cyclic peak stress and hysteresis except for the underestimate of valley stress. We conclude that the QLV model could be used as the material characterization of the esophageal tissue. [DOI: 10.1115/1.2372473] Keywords: quasilinear viscoelasticity (QLV), incremental stress relaxation test, cyclic test, hysteresis, esophagus

The esophagus, like other soft tissues, exhibits nonlinear and anisotropic mechanical properties. As a composite structure, the properties of the outer muscle and inner mucosal layer are different. It is expected that the complex mechanical properties will induce non-homogeneous stress distributions in the wall and nonuniform tissue remodeling. Both are important factors which influence the function of mechanosensitive receptor located in various layers of the wall. Hence, the characterization of the mechanical properties is essential to understand the neuromuscular motion of the esophagus. In this study, the uniaxial tensile tests were conducted along two mutually orthogonal directions of porcine esophageal tissue to identify the directional (circumferential and axial), regional (abdominal, thoracic, and cervical), and layer (muscle and mucosa) variations of the mechanical properties. A structure-based constitutive model, which took the architectures of the tissue's microstructures into account, was applied to describe the mechanical behavior of the esophagus. Results showed that the constitutive model successfully described the mechanical behavior and provided robust estimates of the material parameters. In conclusion, the model was demonstrated to be a good descriptor of the mechanical properties of the esophagus and it was able to facilitate the directional, layer, and regional comparisons of the mechanical properties in terms of the associated material parameters. [DOI: 10.1115/1.2187033] Keywords: strain energy function (SEF), material parameters, collagen, elastin

Abstract: This paper presents a new framework to construct higher-order accurate time-step integration algorithms based on weakly enforcing the differential/integral relation. The dependent variable and its time derivatives are assumed [...]

A full-scale uniplanar completely overlapped tubular K(N) joint specimen is tested to determine the hot spot strains at the joint intersections for the verification of the finite-element (FE) model. The test results reveal that the maximum strain concentration occurs on the through brace saddle near the lap brace. On the chord, the strain distributions perpendicular to the weld toes are linear but on the through brace and the lap brace, they are nonlinear. Based on the FE analysis results, the effects of through brace and lap brace geometric parameters on the joint stress concentration factors (SCF) are found most crucial. The use of the existing Y-joint formulas has considerably underestimated and overestimated the SCF on the through brace saddle near the chord and the lap brace, respectively. At a relatively large gap size, the SCF values at the joint intersection of the through brace and the lap brace are close to that of the Y joint. CE Database keywords: Joints; Stress; Strain.

The aim of this paper is to study the stress concentration factors of doubler plate reinforced tubular T joints subjected to various types of basic loading such as axial tension, axial compression, and in-plane and out-of-plane bending. The finite-element method is adopted in the numerical parametric studies to evaluate the stress distribution. To verify the numerical results, a typical full-scale doubler plate reinforced tubular T joint was fabricated and tested. The strain distributions at the intersection region subjected to various combinations of loading were measured. The results from the experiment compared well with the numerical results. The finite-element modeling techniques were then verified to be accurate and reliable. After the verification, a database was generated from a parametric study by varying some geometrical parameters, such as the wall thickness ratio, diameter ratio, etc. A set of parametric equations with the nondimensional parameters as variables was then established for the evaluation of the stress concentration factors of the doubler plate reinforced tubular T joints. The stress concentration factors on the doubler plate reinforced joints were found lower than the unreinforced joints. DOI: 10.1061/(ASCE)0733-9445(2002)128:11(1399) CE Database keywords: Stress concentration; T Joints; Plates; Axial compression; Bending; Tension.

Quasi-brittle solids usually contain many cracks. When numerical methods are used, it is difficult to simulate all the cracks' behaviors, especially when the crack propagation is included. To surmount the difficulty, a new procedure combining the subdomain boundary element method and the generalized self-consistent scheme is presented. The behavior of a single crack is analyzed first. The obtained information is then used to predict the overall behavior of the cracked solids. The relationship between the overall response of the cracked solids and the growth of wing cracks is established numerically. A cohesive-crack model is used to simulate the fracture process zone of the quasi-brittle solids. Besides, the advancement of the wing crack tip is used as a control variable. An incremental iteration algorithm is developed to trace the growth of the wing (secondary) cracks, which is not known a priori. The influence of the crack angle and the friction coefficient on the effective moduli is also investigated. Finally, a gypsum square plate containing orderly distributed cracks is analyzed to illustrate the adequacy and efficiency of the present procedure. DOI: 10.1061/(ASCE)0733-9399(2002)128:2(240) CE Database keywords: Boundary element method; Solids; Cracking.

A simple and direct analytical formula has been derived to determine the compressive resistance of steel columns subjected to fire conditions. The approach is based on the Rankine principle, which allows the strength and the stability of a steel column at a particular temperature to be separately determined. Here, the evaluation of column strength is based on the rigid-plastic theory, while the stability consideration is based on the elastic-buckling theory. By considering the two factors in this manner, the proposed approach allows for their interaction. One important feature is that the same analytical formula can be used for both axially and eccentrically loaded columns. In addition, the proposed formula does not require any calibrations against test data. The proposed formula has been verified against a set of published column test results and other analytical predictions. The comparison study shows consistently good agreement with both the test and the analytical results.

To ensure structural integrity after modification and/or retrofitting, the behavior of strengthened tubular joints needs to be understood. The finite-element method is a useful tool for studying the problem. However, this numerical technique has to be verified by experimental results before being used extensively. In this paper, the ultimate capacity of doubler plate-reinforced tubular joints is studied. To establish a reference point, a doubler plate-reinforced tubular T-joint was fabricated, instrumented, and tested to failure under axial compression brace loading. The structural behaviors were observed and analyzed. It was found that the ultimate capacity was greatly improved by the inclusion of the doubler plate. The experimental load-displacement curves were compared with the finite-element predictions and good agreement was obtained. The finite-element techniques were then verified and could be used to study the ultimate capacity. A behavioral study was then conducted by applying various types of brace loading and varying different geometric parameters, one at a time.

In this paper, the shear stiffness in the weaker direction of Z-core sandwich panels is studied. The recurrence condition is assumed, and the shear stiffness is derived from the first principle. The contact interaction between the facing plates and the flanges of the Z-sections is considered. Compatibility equations and the shear strain of a typical segment are obtained from the Principle of Virtual Work. Formulas for the shear stiffness in the weaker direction are derived explicitly. It is shown that there are two shear stiffness values associated with the Z-core sandwich panels, depending on the direction of the shear force. The stronger value of a typical panel can be 60% higher than the weaker value. To verify this phenomenon experimentally, two steel sandwich panels with different stiffener spacing were fabricated and tested. Good agreement was obtained between the theoretical predictions and the experimental results.

A C-core sandwich panel consists of two facing plates connected top and bottom to a core of C-shaped stiffeners. Sandwich panels of this type have high bending and shear-stiffness characteristic in the direction of the core. In the transverse direction, however, both stiffness properties are relatively weak, in particular the shear stiffness. In this paper, the shear stiffness in the weaker direction for C-core sandwich panels is derived and studied. Due to the geometry and discontinuity of the core configuration, the shear stiffness in the weaker direction must be derived from the first principle. By assuming the recurrence condition, the writers previously derived an approximate expression for the shear stiffness in the weaker direction. The work described here presents a more accurate formulation, taking into account the contact interaction between the facing plates and the flanges of the C-core stiffeners. The compatibility equations are obtained from Castigliano's second theorem. The shear strain of a typical segment is obtained from the principle of virtual work. Explicit formulation for the shear-stiffness property is given in this paper. The accuracy of the derivation is verified using thick-plate analysis. A detailed comparison with finite-element studies and experimental results is also given. Good agreement is obtained between the theoretical predictions as derived and experimental results.

The completely overlapped joints of the eccentrically braced offshore jackets were investigated both experimentally and numerically. A full-scale specimen was tested under cyclic quasi-static loading. In the test, local buckling was first observed around the lap brace and through-brace intersection. A crack was then developed at the weld toe between the lap brace and the through brace, and the propagation of the crack led to the final failure of the joint. Indicators to assess the performance of the joints were evaluated within the context of seismic resistance. The energy analysis indicated that the local buckling at the intersection area was the main energy-dissipating mechanism. A comparison with an N-joint showed that the completely overlapped joint performed better under seismic loadings. An extensive finite-element analysis showed that increasing the lap brace diameter could improve the hysteresis performance of the joint while changing the gap size and the wall thickness of the through brace would have limited effects.

The analytical solutions of a simple nonlinear equation, e.g., the Duffing equation, can be highly complicated. Homotopy continuation on just one parameter can hardly produce the whole picture, in particular, of the multiple bifurcations in multi-parameter space. This paper reports on the development of the multi-parameter homotopy harmonic balance method for the steady state solutions of a nonlinear vibration problem. The total and tangential stiffnesses with respect to the Fourier components of polynomial nonlinearity are given explicitly. New multiple solutions of the Duffing equation are given for the first time. The period doubling to chaos is interpreted in a new way. Finally, the bifurcation surfaces of folding and period doubling are constructed. [ABSTRACT FROM AUTHOR]

Presents a second-order elastic-plastic hinge method and a finite-element model for the analysis of plane steel frames in fire. Theorems of plastic collapse; Evaluation of beam-column element; Modeling of plastic hinge; Evaluation of chord forces; Evaluation of tangent stiffness matrix; Transformations.