Journal of Engineering Mechanics

Sensitivity analysis is frequently considered an essential component in engineering design. In the design process of engineered structures, the output is implicitly related with the input variables. The Kriging model, one of the most commonly used emulator models, is sometimes used for structure analysis. In order to efficiently estimate the sensitivities of failure probability or statistical moments of performance function with respect to distribution parameters of input variables, the analytical solutions are derived based on the Kriging model. Generally, the Kriging model can be expressed as a tensor product basis function, thus the multivariate integrals can be decomposed into the sum of univariate integrals, which makes it possible to solve the sensitivity of statistical moments with respect to distribution parameters of normal input variables by the properties of kernel functions. Next, the fourth-moment reliability sensitivity method is applied to compute the sensitivity of failure probability analytically. Numerical and engineering examples are introduced to demonstrate the accuracy and efficiency of the derived analytical solution of sensitivity of failure probability.

An anisotropic plasticity model is proposed to describe the fabric effect on sand behavior under both monotonic and cyclic loading conditions within the framework of anisotropic critical state theory. The model employs a cone-shaped bounding surface in the deviatoric stress space and a yield cap perpendicular to the mean stress axis to describe sand behavior in constant mean stress shear and constant stress ratio compression, respectively. The model considers a fabric tensor characterizing the internal structure of sand associated with the void space system and its evolution with plastic deformation. The fabric evolution law is assumed to render the fabric tensor to become codirectional with the loading direction tensor and to reach a constant magnitude of unit at the critical state. In constant stress ratio compression, the final degree of anisotropy is proportional to a normalized stress ratio. An anisotropic variable defined by a joint invariant of the fabric tensor and loading direction tensor is employed to describe the fabric effect on sand behavior in constant mean stress monotonic and cyclic shear. A systematic calibrating procedure of the model parameters is presented. Satisfactory comparison is found between the model simulations and test results on Toyoura sand in both monotonic and cyclic loadings with a single set of parameters. The important role of fabric and fabric evolution in capturing the sand behavior is highlighted. Limitations and potential improvement of the model in describing cyclic mobility of very dense sand and sand behavior in nonproportional loading have been discussed.

Coefficients of crack-tip asymptotic fields are computed using a recently developed weak form quadrature element method (QEM), combined with the subregion generalized variational principle. The variational description of a crack is established by dividing the domain into two regions, the potential energy region and the complementary energy region. Then the weak form QEM is employed to derive a system of algebraic equations. The coefficients are extracted directly from solving the equations. The accuracy, efficiency, and parameter sensitivity of the proposed method are discussed by solving a number of benchmark examples. The computed results are in very good agreement with available analytical or numerical results. The involved parameters can be adjusted according to convergence requirements. Thus, the method enjoys the advantages of straightforwardness and self-adaptivity.

In the study, a two-dimensional closed shell containing fully incompressible fluid is modeled to investigate the behavior of an equatorially anchored deepwater shell storage container. The volume constraint conditions of the shell and contained fluid due to the several external loadings are taken into consideration. The shell, which is installed in deepwater by using anchors at its equator, is assumed to be interacting with the rigid foundation. Since the shell is subjected to periodic anchored forces, the deformed configuration is dependent on the tangential, normal, and circumferential displacements. Therefore, two-dimensional elements are used for investigating the displacements in the shell. Differential geometry is introduced to compute the shell geometry, and small displacement theory is used to calculate the initial strain. The energy functional of the shell and internal fluid are derived from the principle of virtual work in terms of displacements, and are expressed in the appropriate forms. The static deformed configuration of the shell can be obtained by using the nonlinear finite-element method, in which the numerical solutions are solved using an iterative procedure. The validity of the present model and the influence of various geometrical parameters under several external loadings on the shell equilibrium configuration are demonstrated. The results show that the tangential and normal displacements are significant and have an important role in the analysis of a deepwater periodic symmetric shell storage container.

Finite-element methods such as ANSYS are widely used in traditional structural dynamic analysis. The low computational efficiency of ANSYS is a hindrance in finite-element methods when computing the responses of special engineering structures. This paper details an innovative study in which the transfer matrix method of multibody system (MS-TMM) is introduced to analyze the dynamic response of civil engineering structures. Although the responses obtained by the MS-TMM are similar to the responses obtained by ANSYS, ANSYS requires a larger computation time. The results indicate that the MS-TMM can satisfy the computation efficiency and calculation accuracy requirements.

An analytical solution for bending of variable thickness annular sector plates is presented using the multiterm extended Kantorovich method (MTEKM). Utilizing the principle of minimum total potential energy the governing equations are derived based on the first-order shear deformation theory and converted into two sets of coupled ordinary differential equations (ODEs) using MTEKM. Next, the derived sets of ODEs are solved analytically by the application of state-space method. To show the applicability of the present method various examples are investigated. Moreover, solid sector plates as well as rectangular plates are studied as special cases. Results of the present method are compared to those of other methods whenever possible, as well as results obtained by the finite-element method (FEM). It is found that the method proposed here exhibits a high convergence rate as well as presenting accurate results in all cases.

A nonuniform Timoshenko beam model of a building, with piecewise constant properties along the height, is presented, along with an algorithm for structural system identification from earthquake records. The model accounts for shear and flexural deformation, rotatory inertia, and variation of building properties with height. The model stiffness parameters are identified by matching (in the least-squares sense) propagating pulses in impulse response functions. To minimize the effects of soil–structure interaction, the fit is performed on a band excluding the fundamental mode of vibration. This algorithm is a new development in a wave method for structural health monitoring of buildings, intended for use in seismic alert systems to facilitate decision making on evacuation immediately after the earthquake, and for general condition monitoring. The model can also be used with an earthquake early warning system for quick linear response prediction to decide on safe shutdown of sensitive equipment in advance of strong shaking. Identification and response prediction are demonstrated on the north–south response of the Los Angeles 54-story Office Building, a tall, steel-frame building in downtown Los Angeles.

To analyze the hydrodynamic difference between marine structures with and without narrow gaps, a two-dimensional fully nonlinear time-domain numerical wave flume is developed to investigate the hydrodynamics around multiple rectangular-box structures close to one another in waves. In the numerical model, the incident waves are generated by inner-domain sources such that re-reflection at the input boundary can be avoided. The fully nonlinear kinematic and dynamic boundary conditions are satisfied for the instantaneous free surface, and artificial damping is used for the free surface in the gaps to model the viscous effect. The proposed model is first validated against the experimental data for an isolated box and twin- and triple-box systems with narrow gaps. Then extensive numerical experiments are performed to compare the wave heights and wave loads on rectangular boxes with and without narrow gaps. The first comparison is made between the hydrodynamics of each individual box of a multiple-box system and those of an isolated box. The numerical investigation shows that the wave loads on each box in a multiple-box system are greater than those on an isolated box near the resonant wave frequency. Next the hydrodynamics for a multiple-box system are compared with those for a single-monolithic-box system with a total length equal to that of the entire multiple-box system. It is found that the wave height on the weather side of a multiple-box system at resonance is smaller than that of a single-monolithic-box system, and it decreases as the number of gaps increases. The opposite trend is found for the wave height on the lee side.

In this paper, a new kind of activation function using a particular combination of stop and play operators is proposed and used in a feedforward neural network to improve its learning capability in the identification of nonlinear hysteretic material behavior with both stiffness and strength degradation. The new neuron and neural network are referred to as a deteriorating stop and generalized Prandtl neural network, respectively. To show the generality of the proposed neural network, it is trained on several data sets generated by various mathematical models of material hysteresis with and without deterioration as well as on a set of experimental data with very high nonlinearity, including severe damage. In each case, the training is successful, and the generalized Prandtl neural network response precision is very high. Also, using the proposed neural network, a neuro-modeler is designed and used in the dynamic analysis of a one-story shear frame under seismic loads with severe damage. A comparison of the results shows that the generalized Prandtl neural network type of the neuro-modeler is more successful than the previously proposed Prandtl neural network type.

In multiphase particulate composites, the deviation and mismatch of the elastic moduli of different particles may significantly affect the overall mechanical performance of the composites. This study investigates the effects of such deviations on the macroscopic properties of multiphase composites via an iterative micromechanics-based method. The elastic properties of the particles are assumed to obey certain statistical distributions. In the proposed iterative method, the composites are divided into multiple two-phase composites and their strain concentration tensors are derived by means of the inclusion matrix–reference medium model, which is a modification of the generalized self-consistent method. Iterative solutions are established that take into account the effects of the variation in the elastic properties of the particles in terms of the effective shear and bulk moduli. The findings show that the proposed iterative method converges quickly and that the results agree well with the experimental data for three-phase composites. In addition, the model indicates that the variation in the elastic properties of the particles does have a significant effect on the effective moduli of the composites.

Starting with static and dynamic micropolar linear plane stress elasticity, and applying Timoshenko beam kinematics with axial stretch, a mixed micropolar small-strain beam finite element (FE) formulation results. The mixed formulation is shown to be convergent upon mesh refinement under static and dynamic loading. The acceleration form of the Newmark family of time integration methods is applied to integrate the coupled hyperbolic linear governing equations. Instantaneous axial and transverse step forces are applied and released to analyze the free longitudinal and transverse vibrations with the mixed formulation FE implementation. The transverse displacement and rotational degrees of freedom (DOF) are coupled, but the axial displacement is decoupled from the rotational DOF because the first area moment of inertia $Q$ is zero. Applied sinusoidal axial and transverse forces lead to axial and transverse displacement and rotational wave patterns that are a combination of low and high frequency waves. The effect of length scale $\ell$ on elastic couple modulus ${\gamma }^{\ell }$ and spin inertia $j$ is demonstrated, which shows a transverse and rotational stiffening through ${\gamma }^{\ell }$ upon increasing $\ell$, yet a decreasing frequency as $j$ also increases with $\ell$.

In this paper, a three-dimensional numerical wave model is applied to simulate solitary wave run-up and breaking on a plane beach, as well as the resulting breaking-wave force exerted on a single pile located at different elevations on the beach. The model employed is based on Reynolds–averaged Navier-Stokes (RANS) equations with a $k\text{-}\epsilon$ model for turbulence closure. The model is validated using experimental data on breaking solitary wave run-up on a plane beach, time history of the wave force on a cylinder, and wave-pile interaction on a sloping bottom. After model validation, the wave model is applied to simulate wave-pile interaction with the pile located at seven different elevations on the plane beach. Snapshots of wave-pile interaction, as well as the time history of breaking-wave force on the pile, are obtained and analyzed. The variations in breaking-wave force with elevation of the pile are also discussed.

This paper presents a coupled wave–vegetation model for simulating the interaction between water waves and submerged flexible plants. The balance of forces for the vegetation motion includes buoyancy, damping, stiffness of the vegetation, and gravity as restoring forces, and drag and inertia as driving forces. The governing equation for vegetation motion is solved by the high-order finite element method (FEM) together with an implicit time differencing scheme. The results of the vegetation model exhibit a fourth-order convergence rate. The vegetation-induced drag and inertia are introduced into the wave model as a source term in the momentum equation. This coupled model is rigorously verified by comparing numerical results with theoretical solutions for single swaying vegetation cases and with experimental data for large-scale swaying vegetation cases. Excellent agreement is achieved. A scaling analysis is performed on the governing equation for vegetation motion to understand the importance of each force involved in the vegetation vibration. For cases in which damping becomes significant compared with other restoring forces, a theoretical relationship between movements of vegetation stem and water particle is derived, and a dimensionless parameter, incorporating characteristics of waves and material as well as geometric properties of vegetation, is obtained. The vegetation deformation model developed in this paper can be coupled with other wave models to simulate wave and vegetation interactions.