• Coupled systems mechanics
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• v.4 no.1
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• pp.1-18
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• 2015

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.

• Interaction and multiscale mechanics
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• v.7 no.1
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• pp.525-542
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• 2014

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.

• Structural Engineering and Mechanics
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• v.10 no.2
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• pp.111-123
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• 2000

An asymptotic solution for snap-through buckling of single-layer squarely-reticulated shallow spherical shells continuously supported on springs is developed in this paper. Based on the fundamental governing equations and boundary conditions, a nondimensional analytical expression associated with the external load, stiffness of spring and central transverse displacement (deflection) is derived with the aid of asymptotic iteration method. The effects of stiffness of spring and characteristic geometrical parameter on buckling of the structures are given by the analyses of numerical examples. In a special case, for reticulated circular plates, the influence of stiffness of spring on the characteristic relation between load and deflection is also demonstrated.

• Proceedings of the Korea Technical Association of the Pulp and Paper Industry Conference
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• 2002.05a
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• pp.76-84
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• 2002

Fracture toughness was considered as one of the good estimates of the paper break tendency of paper web in the press room. Paper break on the paper machine is caused by many factors such as paper machine irregular vibrations, impurities in the fiber furnish, shives, and so on. On the paper machine, the solid content of paper web is changing very rapidly from less than 1% to over 95%. We tried to measure the fracture toughness of paper web at different solid contents for providing the fundamental knowledge of paper break. Stretches of wet web were also measured and compared to the fracture toughness changes. Four different fiber furnishes (SwBKP, HwBKP, ONP, and OCC) were refined to different degrees, and at different solid contents (40%, 60%, 80%, and 95%), their fracture toughnesses were measured. Two fracture toughness measurement methods (essential work of fracture and Tryding's load-widening method) were used, and we found they gave identical results. The stretch curves of the wet webs against the axis of solid contents were very similar to the fracture toughness curves of those.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.33 no.5
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• pp.37-44
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• 2001

Fracture toughness was considered as one of the good estimates of the paper break tendency of paper web in the press room. Paper break on the paper machine is caused by many factors such as paper machine irregular vibrations, impurities in the fiber furnish, shives, and so on. On the paper machine, the solid content of paper web is changing very rapidly from less than 1% to over 95%. We tried to measure the fracture toughness of paper web at different solid contents for providing the fundamental knowledge of paper break. Stretches of wet web were also measured and compared to the fracture toughness changes. Four different fiber furnishes (SwBKP, HwBKP, ONP, and OCC) were refined to different degrees, and at different solid contents (40%, 60%, 80% and 95%), their fracture toughnesses were measured. Two fracture toughness measurement methods (essential work of fracture and Tryding's load-widening method) were used, and we found they gave identical results. The stretch curves of the wet webs against the axis of solid contents were very similar to the fracture toughness curves of those.

• Structural Engineering and Mechanics
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• v.78 no.4
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• pp.413-423
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• 2021

Piers are the main lateral force-resisting members of high-speed railway (HSR) bridges used in China and are characterized by low axial load ratios, low longitudinal reinforcement ratios, low stirrup ratios, and high shear span ratios. It is well known that flexural, flexural-shear, and shear failures of piers may occur during an earthquake. In this study, a new shear strength model was developed to simulate the seismic failure of HSR solid piers accurately. First, low cyclic-loading test data of solid piers obtained in recent years were collected to set up a database for model verification. Second, based on the test database, the applicability of existing shear strength models was evaluated. Finally, a new shear strength model for HSR solid piers with round-ended cross-sections was derived based on the truss model and ultimate equilibrium theory. In comparison with existing models, it was demonstrated that the proposed model could be used to predict the shear strength of HSR piers more accurately.

• Coupled systems mechanics
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• v.11 no.5
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• pp.439-458
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• 2022

Over-coating is one of the most popular engineering practices to strengthen Reinforced Concrete (RC) structures, due to the relative quickness and ease of construction. It consists of an external coat bonded to the outer surface of the structural RC element, either by the use of chemical adhesives, mechanical anchor bolts or simply mortar injection. In contrast to these constructive advantages, the numerical estimation of the bearing capacity of the strengthened reinforced concrete element is still complicated, not only for the complexity of modelling a flexible membrane or plate attached to a quasi-rigid solid, but also for the difficulties that raise of simulating any potential delamination between both materials. For these reasons, the standard engineering calculations used in the practice remain very approximated and clumsy. In this work, we propose the formulation of a new 2D solid-layer finite element capable to link a solid body with a flexible thin layer, as it were the "skin" of the body, allowing the potential delamination between both materials. In numerical terms, this "skin" element is intended to work as a transitional region between a solid body (modelled with a classical formulation of a standard quadrilateral four-nodes element) and a flexible coat layer (modelled with cubic beam element), dealing with the incompatibility of Degrees-Of-Freedom between them (two DOF for the solid and three DOF for the beam). The aim of the solid-layer element is to simplify the mesh construction of the strengthened RC element being aware of two aspects: a) to prevent the inappropriate use of very small solid elements to simulate the coat; b) to improve the numerical estimation of the real bearing capacity of the strengthened element when the coat is attached or detached from the solid body.

• Coupled systems mechanics
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• v.12 no.6
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• pp.481-501
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• 2023

Over-coating is one of the most popular engineering practices to strengthen Reinforced Concrete (RC) structures, due to the relative quickness and ease of construction. It consists of an external coat bonded to the outer surface of the structural RC element, either by the use of chemical adhesives, mechanical anchor bolts or simply mortar injection. In contrast to these constructive advantages, the numerical estimation of the bearing capacity of the strengthened reinforced concrete element is still complicated, not only for the complexity of modelling a flexible membrane or plate attached to a quasi-rigid solid, but also for the difficulties that raise of simulating any potential delamination between both materials. For these reasons, the standard engineering calculations used in the practice remain very approximated and clumsy. In this work, we propose the formulation of a new 2D solid-layer finite element capable to link a solid body with a flexible thin layer, as it were the "skin" of the body, allowing the potential delamination between both materials. In numerical terms, this "skin" element is intended to work as a transitional region between a solid body (modelled with a classical formulation of a standard quadrilateral four-nodes element) and a flexible coat layer (modelled with cubic beam element), dealing with the incompatibility of Degrees-OfFreedom between them (two DOF for the solid and three DOF for the beam). The aim of the solid-layer element is to simplify the mesh construction of the strengthened RC element being aware of two aspects: a) to prevent the inappropriate use of very small solid elements to simulate the coat; b) to improve the numerical estimation of the real bearing capacity of the strengthened element when the coat is attached or detached from the solid body.

• Structural Engineering and Mechanics
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• v.14 no.4
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• pp.455-472
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• 2002

The paper involves the study on the elastic and elasto-plastic stress wave propagation in the 1-D and 2-D solid media. The Smooth Particle Hydrodynamics equations governing the elastic and elasto-plastic large deformation dynamic response of solid structures are presented. The proposed additional stress points are introduced in the formulation to mitigate the tensile instability inherent in the SPH approach. Both incremental rate approach and leap-frog algorithm for time integration are introduced and the new solution algorithm is developed and implemented. Two examples on stress wave propagation in aluminium bar and 2-D elasto-plastic steel plate are included. Results from the proposed SPH approach are compared with available analytical values and finite element solutions. The comparison illustrates that the stress wave propagation problems can be effectively solved by the proposed SPH method. The study shows that the SPH simulation is a reliable and robust tool and can be used with confidence to treat transient dynamics such as linear and non-linear transient stress wave propagation problems.

• Coupled systems mechanics
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• v.7 no.5
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• pp.583-610
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• 2018

This paper discusses the issues associated with modeling frictional contact between solid bodies undergoing large deformations. The most common model for friction on contact interfaces in solid mechanics is the Coulomb friction model, in which two distinct responses are possible: stick and slip. Handling the transition between these two phases computationally has been a source of algorithmic instability, lack of convergence and non-unique solutions, particularly in the presence of large deformations. Most computational models for frictional contact have used penalty or updated Lagrangian approaches to enforce frictional contact conditions. These two approaches, however, present some computational challenges due to conditioning issues in penalty-type implementations and the iterative nature of the updated Lagrangian formulation, which, particularly in large simulations, may lead to relatively slow convergence. Alternatively, a plasticity-inspired implementation of frictional contact has been shown to handle the stick-slip conditions in a local, algorithmically efficient manner that substantially reduces computational cost and successfully avoids the issues of instability and lack of convergence often reported with other methods (Laursen and Simo 1993). The formulation of this approach, however, has been limited to the small deformations realm, a fact that severely limited its application to contact problems where large deformations are expected. In this paper, we present an algorithmically consistent formulation of this method that preserves its key advantages, while extending its application to the realm of large-deformation contact problems. We show that the method produces results similar to the augmented Lagrangian formulation at a reduced computational cost.