Journal of Engineering Mechanics

Analysis of the bending and stretching problem of doubly curved laminated shells is formulated on the basis of three-dimensional elasticity. The basic idea underlying the approach is to make the formulation amenable to asymptotic analysis, which otherwise would be too complicated to deal with. In the formulation, the basic field equations are first rearranged into equations in terms of displacements and transverse stresses, and then they are made dimensionless by proper scaling of the field variables. By means of asymptotic expansion the recast equations can be decomposed into recurrent sets of differential equations at various levels. It turns out that the asymptotic equations can be integrated in succession, leading to the two-dimensional equations in the classical laminated shell theory (CST) at each level. Higher-order corrections as well as the first-order solution can be determined by treating the CST equations at multiple levels in a systematic and consistent way. The essential feature of the present analysis is that accurate three-dimensional elasticity solution can be determined by solving the CST equations in an adaptive and hierarchic manner without treating the layers individually. Several illustrative examples are given to demonstrate the performance of the theory.

The paper describes a new finite element, derived from the classical constant strain element, in the context of localization analysis of elastic-plastic materials. The formulation is based on the “enhanced strain” concept, which is extended to include regularized displacement discontinuities. As a result, the localization band is embedded within the element and the conventional displacement topology is preserved. The major advantage, as compared to the interelement representation, is that advanced mesh (re)alignment strategies are totally avoided and unstructured meshes are sufficient. An interesting feature of the element is that the condition for existence of an internal element discontinuity is identical to the classical condition for band-shaped localization. The element is combined with a cohesive crack model that is based on the Rankine criterion and a well-established calibration technique to achieve an objective response in the post peak softening range in terms of the dissipated (fracture) energy. Results from finite-element analyses of a notched concrete plate are provided.

A micromechanical damage model for a brittle solid capable of taking into account the effect of high loading rate (in the form of stress-rate) is presented. Although, this model is applicable to any particulate brittle solid, concrete is given primary consideration. An existing self-consistent rate-insensitive model is modified and extended to induce rate dependency of concrete type material with preexisting damages (cracks). The variations of several fracture mechanics parameters of solid, viz., stress intensity factors, fracture toughnesses, etc., under the influence of high loading rates were given primary consideration. The process of crack evolution in a particulate cracked solid under tensile and compressive stress-field has been thoroughly considered along with all possible situations that may arise. Crack kinking and nucleation are considered for both tensile and compressive stress-field. The resulting rate-sensitive micromechanical damage model has been codified and several experiments have been replicated to validate it.

A three-dimensional model is developed for the simulation of the pounding response of two or more adjacent buildings during earthquakes. The contact-impact problem is treated by the Lagrange multiplier method. The structures are modeled as multiple-degree-of-freedom systems with finite elements and with the possibility of contact between slabs or slabs and columns. Contact points are not known a priori, and are located through a searching procedure among the candidate contact surfaces. The dynamic equilibrium equations of contact follow an iterative formulation at each time step to account for the current contact conditions. With this three-dimensional idealization, the effect of various in-plan configurations of adjacent buildings as well as the induced deformations due to torsion during pounding are investigated for two real earthquake motions.

A variable-node flat shell element is presented. The element has a variable number of midside nodes and each node has a drilling freedom. The element has been developed basically by combining a membrane element with drilling degrees of freedom and a plate bending element. Thus, the element possesses six degrees of freedom per node that, in addition to improvement of the element behavior, permit an easy connection to other six-degrees-of-freedom per node elements. By introducing the variable-node elements that have physical midside nodes, some difficulties associated with connecting the different layer patterns in the common adaptive h -refinement on quadrilateral mesh, such as imposing displacement constraints on irregular nodes to enforce the interelement compatibility can be easily overcome. Detailed numerical studies show the excellent performance of the new shell elements developed in this study.

This paper describes a new method for representing hydrodynamic drag forces on a marine structure subjected to random waves. It is shown that the obtained force representation has the correct statistical properties to good approximation. A fair agreement can also be obtained between the spectral density of the force representation and that of the original drag force. The distinct advantage of the proposed representation is that it becomes possible to carry out a dynamic analysis of a linear structure in the frequency domain using available techniques, which are part of a larger packet that includes efficient tools for providing detailed statistical information about the response process. This has implications toward more efficient analyses of, for example, long-term fatigue of offshore structures.

A warping solution for prismatic thin-walled orthotropic composite beams is presented. For beam-wall macroelements, the macro approach solution is applied to obtain the displacements as a sum of polynomial plus Fourier functions. The kinematics of a beam-wall are obtained from a generalized plane stress solution. Constitutive equations that account for both slender and stiffened FRP sections are proposed. A fast converging continuous closed-form solution is obtained for the macroelement. The wall displacement field is evaluated in terms of nodal line parameters. Elastic coefficients that account for warping effects are introduced to provide a mechanics interpretation of the formulation. The macroelement assembling technique is illustrated by presenting an explicit warping solution for bending of box beams. The warping solution is correlated with existing analytical solutions. An expression for both the effective width and the effective longitudinal modulus variation in flanges of box beams is presented. A design equation consistent with current practice is proposed.

This paper proposes a new and less laborious version of the size-effect method for measuring the fracture energy or fracture toughness of concrete as well as other nonlinear fracture characteristics, such as the effective length of fracture process zone or critical crack-tip opening displacement. The size-effect method, based on the size-effect law, is the simplest to carry out because only the maximum loads of specimens need to be measured. No measurements of postpeak deflection and unloading stiffness, nor observations of crack-tip location, are needed; the testing machine need not be very stiff, and there is no need for closed-loop displacement control. The simplicity of the method makes it suitable not only for the laboratory but also for field quality control. In the original version of the size-effect method, notched specimens of different sizes are tested. The proposed new version further simplifies testing by allowing the use of notched specimens of only one size. The idea is to supplement the one-size notched-beam tests with an evaluation of the maximum load value for specimens with a zero-brittleness number. There are two types of methods that will achieve this. In one type of method, zero-brittleness data are obtained by using plastic limit analysis based on the modulus of rupture or compression strength of concrete to calculate the limiting nominal strength for zero specimen size. In the second type of method, zero-brittleness data are obtained by testing the maximum loads of notchless specimens of the same size. The former type leads to simpler calculations but has the drawback that the material strength to calculate the maximum load for zero size depends on specimen geometry. Both types of the zero-brittleness version of the size-effect method are validated by previously reported test data. The proposed method should also be applicable to other quasibrittle materials such as rock, ice, tough ceramics, and brittle composites.

This paper examines the rationale behind the semiempirical formulation of a generalized viscoplastic fluid (GVF) model in the light of the Reiner-Rivlin constitutive theory and the viscoplastic theory, thereby identifying the parameters that control the rheology of granular flow. The shear-rate number ( N ) proves to be among the most significant parameters identified from the GVF model. As N → 0 and N →∞, the GVF model can reduce asymptotically to the theoretical stress versus shear-rate relations in the macroviscous and grain-inertia regimes, respectively, where the grain concentration ( C ) also plays a major role in the rheology of granular flow. Using available data obtained from the rotating-cylinder experiments of neutrally buoyant solid spheres dispersing in an interstitial fluid, the shear stress for granular flow in transition between the two regimes proves dependent on N and C in addition to some material constants, such as the coefficient of restitution. The insufficiency of data on rotating-cylinder experiments cannot presently allow the GVF model to predict how a granular flow may behave in the entire range of N ; however, the analyzed data provide an insight on the interrelation among the relevant dimensionless parameters.