Modelling of laser beam spot-weld using 2-D hybrid crack finite elements

Laser beam spot-welding is widely applied to join sheet metals for automotive components especially for thinsheet components in automotive industries. The spot welds in such metallic structures contribute a lot to the integrated strength and fatigue life for the whole structures and they are responsible for their damage or collapse in some loading cases. In this paper, the 2-D hybrid special finite elements each containing an edge crack are employed to study the fracture behaviors of laser beam spot-welds. Hence the calculation accuracy in the vicinity of crack tips is ensured, and a better description of stress singularity with only one hybrid element surrounding one crack is provided. The numerical modeling for laser beam spot-welds subjected to three typical modes ofloadings including tension-lap, shear-lap and angle-clip can be greatly simplified with the applications of such elements. Three specimens under lap-shear, lap-tension and angle clip are devised and analyzed respectively, and main fracture parameters such as stress intensity factors and the initial direction of crack growth are obtained through tinite element analyses. The computed results ti'om numerical examples demonstrate the validity and versatility of the proposed modeling.

A family of simple and robust finite elements for linear and geometrically nonlinear analysis of laminated composite plates

A family of simple, displacement-based and shear-flexible triangular and quadrilateral flat plate/shell elements for linear and geometrically nonlinear analysis of thin to moderately thick laminate composite plates are introduced and summarized in this paper.

The developed elements are based on the first-order shear deformation theory (FSDT) and von-Karman’s large deflection theory, and total Lagrangian approach is employed to formulate the element for geometrically nonlinear analysis. The deflection and rotation functions of the element boundary are obtained from Timoshenko’s laminated composite beam functions, thus convergence can be ensured theoretically for very thin laminates and shear-locking problem is avoided naturally.

The flat triangular plate/shell element is of 3-node, 18-degree-of-freedom, and the plane displacement interpolation functions of the Allman’s triangular membrane element with drilling degrees of freedom are taken as the in-plane displacements of the element. The flat quadrilateral plate/shell element is of 4-node, 24-degree-of-freedom, and the linear displacement interpolation functions of a quadrilateral plane element with drilling degrees of freedom are taken as the in-plane displacements.

The developed elements are simple in formulation, free from shear-locking, and include conventional engineering degrees of freedom. Numerical examples demonstrate that the elements are convergent, not sensitive to mesh distortion, accurate and efficient for linear and geometric nonlinear analysis of thin to moderately thick laminates.

Recent advances of finite elements for laminated composite plates

A large amount of finite elements have been developed for finite element analysis of laminated composite plates. The laminated plate theories are reviewed and summarized in this paper. The focus of this review is on the recently developed laminated finite elements since 1990. The 2-D triangular and quadrilateral displacement-based and mixed/hybrid-based finite element models, which were developed based on the first-order shear deformation theories, the higher-order shear deformation theories, the zig-zag theories and the global-local higher-order deformation theories, and the layer-wise laminated plate theories are reviewed in this paper and also their related patents. Finally, some points on the development of the laminated finite elements are summarized.

Hybrid special finite element method for bi-material crack

In the paper, two novel 2-D hybrid special finite elements each containing an interfacial edge crack, which lies along or vertical to the interface between two materials, are developed. These proposed elements can assure the high precision especially in the vicinity of crack tip and provide a better description of its singularity with only one hybrid element surrounding one interfacial crack, thus, the numerical modeling of fracture analysis on bi-material crack can be greatly simplified. Numerical examples are provided to demonstrate the validity and versatility of the proposed method.

Laminated plate elements based on higher-order shear deformation theories

Efficient and accurate finite elements are crucial for finite element analysis to provide adequate prediction of the structural behavior. A large amount of laminated plate elements have been developed for finite element analysis of laminated composite plates based on the various lamination theories. A recent and complete review of the laminated finite elements based on the higher-order shear deformation theories, including the global higher-order theories, zig-zag theories and the global-local higher-order theories is presented in this paper. Finally some points on the development of the laminated plate elements are summarized.

Hybrid neural network—finite element river flow model

Results obtained from a hybrid neural network—finite element model are reported in this paper. The hybrid model incorporates artificial neural network (ANN) nodes into a numerical scheme, which solves the two-dimensional shallow water equations using finite elements (FE). First, numerical computations are carried out on the entire numerical model, using a larger mesh. The results from this computation are then used to train several preselected ANN nodes. The ANN nodes model the response for a part of the entire numerical model by transferring the system reaction to the location where both models are connected in real time. This allows a smaller mesh to be used in the hybrid ANN-FE model, resulting in savings in computation time. The hybrid model was developed for a river application, using the computational nodes located at the open boundaries to be the ANN nodes for the ANN-FE hybrid model. Real-time coupling between the ANN and FE models was achieved, and a reduction is CPU time of more than 25% was obtained.

Modeling of voids/cracks and their interactions

Numerical modeling of a two-dimensional elastic body containing multiple voids/cracks to study the interaction between these defects can be  significantly simplified by developing special finite elements, each containing an internal circular/elliptic hole or a slit crack. These finite elements are developed using complex potentials and the conformal mapping technique. The elements developed can be divided into two categories, namely, the semi-analytic-type and hybrid-type elements. The latter element type is an improved version of the former due to the implementation of displacement continuity along the inter-element boundary. All the proposed elements can be easily combined with the conventional displacement elements, such as isoparametric elements, to analyze the above-mentioned problems without using complicated finite element meshes. Numerical examples have been employed to illustrate the modeling of voids/cracks and their interactions. The results obtained using the semi-analytic-type elements are in good agreement with the theoretical results, and the corresponding results obtained using the hybrid-type elements show an improvement of the agreement with the theoretical results. However, the former element type is much easier to construct.

Investigation of effective material properties in composites with internal defect or reinforcement particles

This paper is concerned with the investigation of the effective material properties of internally defective or particle-reinforced composites. An analysis was carried out with a novel method using the two-dimensional special finite element method mixing the concept of equivalent homogeneous materials. A formulation has been developed for a series of special finite elements containing an internal defect or reinforcement in order to assure the high accuracy especially in the vicinity of defects or reinforcements. The adoption of the special finite element can greatly simplify numerical modeling of particle-composites. The numerical result provides the effective material properties of particle-reinforced composite and explains that the size of particles has great influence on the material properties. Numerical examples also demonstrate the validity and versatility of the proposed method by comparing with existing results from literatures.

Numerical modeling of interactions between a macro-crack and a cluster of micro-defects

The interactions between a macro-crack and a cluster of micro-defects are studied numerically by using a series of special finite elements each containing a defect. These special finite elements, which contain defects such as holes, cracks, and inhomogeneities, are developed based on the hybrid displacement, complex potential and conformal mapping techniques. These hybrid-type elements can be used together with the conventional finite elements without any difficulty. Thus, simple finite element models can be devised to study the interactions between a macro-crack and a cluster of micro-defects. In this paper, the mathematical and finite element modeling procedures for the study of the above-mentioned problems are presented.

Evaluation of effective material properties of composite materials using special FEM

In the present paper, a novel method using the special 2D finite element method (FEM) and the concept of equivalent homogeneous materials has been employed to evaluate the effective material properties of composites. Special 2D finite elements containing an internal defect or reinforcement have been well developed in order to greatly simplify the numerical modeling of composites. It can assure the high precision especially in the vicinity of defects or reinforcements in composite materials. Some numerical examples will be provided to demonstrate the validity and versatility of the proposed method by comparing the existing results from other literatures.

Comparison of mechanical behaviour of thin film simulated by discrete dislocation dynamics and continuum crystal plasticity

3D finite element simulations of 9-grain multicrystalline aggregates are performed within the framework of the classical continuum crystal plasticity and discrete dislocation dynamics. The results are processed in a statistical way by ensemble averaging. The comparison is made at three levels: macroscopic stress–strain curves, average stress values per grain, local values of stress and plastic strain. The comparison shows that some similarities are observed in the stress and strain distributions in both simulations approaches. But there are also large discrepancies caused by the discrete nature of plasticity in DDD. The DDD simulations provide higher stress levels in the aggregate due to the small number of dislocation sources and to the stress field induced by individual dislocations.

Trench stability under bentonite pressure in purely cohesive clay

Trench stability is a conventional geotechnical problem; however, current evaluations are often based entirely on empiricism. This paper uses numerical finite-element upper and lower bound limit analysis to produce stability charts for two-dimensional and three-dimensional homogeneous and inhomogeneous undrained diaphragm wall trenches. Using the limit theorems cannot only provide a simple and useful way of analyzing the stability of the trench, but also avoid the shortcomings and arbitrary assumptions underpinning the limit equilibrium method. By considering the effects from the bentonite slurry pressures, the collapse load in this study has been bracketed to within ±8.5 or better by the numerical upper and lower bound limit analyses. The chart solutions can be used to predict either the critical depth or the safety factor of the trench and provide a convenient tool for preliminary designs by practicing engineers. © 2014 American Society of Civil Engineers.