Abstract: Problem statement: **The** use **of** fracture mechanics techniques in **the** assessment **of** performance and reliability **of** structure is on increase and **the** prediction **of** **crack** **propagation** in structure play important part. **The** **finite** **element** method is widely used for **the** evaluation **of** SIF for various types **of** **crack** configurations. Source code program **of** two-dimensional **finite** **element** model had been developed, to demonstrate **the** capability and its limitations, in predicting **the** **crack** **propagation** trajectory and **the** SIF values under linear elastic fracture **analysis**. Approach: Two different geometries were used on this **finite** **element** model in order, to analyze **the** reliability **of** this program on **the** **crack** **propagation** in linear and nonlinear elastic fracture mechanics. These geometries were namely; a rectangular plate with **crack** emanating from square-hole and Double Edge Notched Plate (DENT). Where, both geometries are in tensile loading and under mode I conditions. In addition, **the** source code program **of** this model was written by FORTRAN language. Therefore, a Displacement Extrapolation Technique (DET) was employed particularly, to predict **the** **crack** propagations directions and to, calculate **the** Stress Intensity Factors (SIFs). Furthermore, **the** mesh for **the** **finite** elements was **the** unstructured type; generated using **the** advancing front method. And, **the** global h-type adaptive mesh was adopted based on **the** norm stress error estimator. While, **the** quarter- point singular elements were uniformly generated around **the** **crack** tip in **the** form **of** a rosette. Moreover, make a comparison between this current study with other relevant and published research study. Results: **The** application **of** **the** source code program **of** 2-D **finite** **element** model showed a significant result on linear elastic fracture mechanics. Based on **the** findings **of** **the** two different geometries from **the** current study, **the** result showed a good agreement. And, it seems like very close compare to **the** other published results. Conclusion: A developed a source program **of** **finite** **element** model showed that is capable **of** demonstrating **the** SIF evaluation and **the** **crack** path direction satisfactorily. Therefore, **the** numerical **finite** **element** **analysis** with displacement extrapolation method, had been successfully employed for linear-elastic fracture mechanics problems.

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For full 3D elasticity formulations for vibration and linear dynamic **analysis** **of** FGM shells, one find **the** work **of** Vel and Batra (2004) based on three dimensional exact solutions for free and forced vibrations **of** simply supported FGM rectangular plates. In Asemi et al. (2014) **the** static and dy- namic analyses **of** FGM skew plates are obtained based on **the** three-dimensional theory **of** elastici- ty. Graded elements, **the** principle **of** minimum energy and Rayleigh-Ritz energy method are used. Using 3D elasticity model, Nguyen and Nguyen-Xuan (2015) proposed an efficiently computational tool based on an isogeometric **finite** **element** formulation for static and dynamic response **analysis** **of** FGM plates.

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which is gradually increased to near **the** ultimate load that may be sustained by **the** pipe. **The** pipe is modelled as an elasto-plastic material using **the** Von Mises yield criterion which is normally used for metallic **materials**[2]. **The** specification **of** **the** load in several increments enables **the** spread **of** **the** plasticity to occur gradually and its effect on **the** stress distribution to be assessed. Key words: **finite** **element** **analysis**, elastic-plastic behavior, thin walled pipe equivalent stress, TWT.

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But there are only a few works devoted to direct investigation **of** temperature evolution at fatigue **crack** tip. At present, it is well known that in **materials** under cyclic deformation, fatigue cracks are initiated in **the** area **of** plastic deformation localization and lead to an intensive heat dissipation [4]. It makes possible **the** early detection **of** **crack** initiation by infrared thermography [5]. **The** infrared thermography can be also applied during mechanical tests in order to obtain detailed information about **the** process **of** structure evolution, damage accumulation and damage-fracture transition in solids [6-8]. **The** investigation **of** **the** heat dissipation at **the** fatigue **crack** tip allows one to develop an effective method for determination **of** **the** linear fracture mechanics parameters in a wide range **of** stress intensity and, as a consequence, gives a way **of** monitoring **of** critical state **of** **crack**. **The** solution **of** this problem requests an **analysis** **of** solutions **of** nonlinear problems **of** plasticity theory and experimental investigation **of** plastic deformation localization at **crack** tip.

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Structural optimization using computational tools has be- come a major research field in recent years. Methods com- monly used in structural **analysis** and optimization may de- mand considerable computational cost, depending on **the** problem complexity. Therefore, many techniques have been evaluated in order to diminish such impact. Among these various techniques, Artificial Neural Networks (ANN) may be considered as one **of** **the** main alternatives, when com- bined with classic **analysis** and optimization methods, to reduce **the** computational effort without affecting **the** final solution quality. Use **of** laminated composite structures has been continuously growing in **the** last decades due to **the** ex- cellent mechanical properties and low weight characterizing these **materials**. Taken into account **the** increasing scien- tific effort in **the** different topics **of** this area, **the** aim **of** **the** present work is **the** formulation and implementation **of** a computational code to optimize manufactured complex lam- inated structures with a relatively low computational cost by combining **the** **Finite** **Element** Method (FEM) for structural **analysis**, Genetic Algorithms (GA) for structural optimiza- tion and ANN to approximate **the** **finite** **element** solutions. **The** modules for linear and geometrically non-linear static fi- nite **element** **analysis** and for optimize laminated composite plates and shells, using GA, were previously implemented. Here, **the** **finite** **element** module is extended to analyze dy- namic responses to solve optimization problems based in fre- quencies and modal criteria, and a perceptron ANN module is added to approximate **finite** **element** analyses. Several ex- amples are presented to show **the** effectiveness **of** ANN to approximate solutions obtained using **the** FEM and to re- duce significatively **the** computational cost.

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series **of** 3D stress analyses by **finite** **element** method have been made on SENT specimen using ABAQUS 6.5 [13] **finite** **element** software. **The** geometry **of** **the** specimen considered in this **analysis** is shown in Fig.1. **Finite** **element** computations were carried out considering only one half **of** **the** specimen due to **the** symmetry. **The** **analysis** domain is descritized using 20-noded isoparametric 3D **solid** reduced integration elements. These types **of**

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Fatigue is still one **of** **the** main concerns when dealing with mechanical components failure. While it is fundamental to experimentally determine **the** fatigue material behavior using standard specimens, testing large and complex component geometries can be complicated. In these cases, **the** **Finite** **Element** Method can be a cost-effective solution but developing fatigue **crack** growth models is still a complicated task. In order to solve this problem, an algorithm for automatic **crack** **propagation** was developed. Using three different modules, **the** algorithm can generate a complex **Finite** **Element** Method model including a fatigue **crack**; solve this model considering complex loading conditions, by applying **the** superposition method; and calculate **the** fatigue **crack** **propagation** rate, using it to update **the** original model. In order to benchmark this solution two different problems were analyzed, a modified compact tension specimen and a cruciform specimen. By modifying **the** compact tension specimen hole location and simulating an initial **crack**, it was possible to understand how mixed mode conditions influence **the** fatigue **crack** path. Different load ratios and initial **crack** directions on **the** cruciform specimen were analyzed. Increasing **the** load ratio will increase **the** **crack** deflecting angle. **The** obtain solutions were compared with experimental results, showing good agreement. Therefore **the** developed algorithm can be used to predict **the** fatigue **crack** growth behavior on complex geometries and when different types **of** loads are applied to **the** component.

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While transferring power from driving to driven sprocket, chain exerts high load on sprocket teeth.So, maximum loads acting on teeth are calculated.Stress induced due to load should be less than **the** yield stress **of** **the** material. If stress becomes more than yield stress **of** material then there is a possibility **of** failure. Hence static **analysis** was performed to ensure that **the** proposed design has factor **of** safety greater than one. Also due to cyclic load acting on **the** sprocket from chain, it is important to test **the** sprocket for fatigue loading. In fatigue **analysis** fatigue life **of** sprocket is calculated and it is ensured that **the** minimum fatigue life is higher for safe use **of** sprocket for sufficient time period. After **the** minimum fatigue life, **crack** in **the** component initiated, which further increases with time and leads to failure **of** component. Therefore it is important for any component to have sufficient fatigue life.

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In this contribution modeling and simulation **of** surface acoustic waves (SAW) sensor using **finite** **element** method will be presented. SAW sensor is made from piezoelectric GaN layer and SiC substrate. Two different **analysis** types are investigated - modal and transient. Both analyses are only 2D. **The** goal **of** modal **analysis**, is to determine **the** eigenfrequency **of** SAW, which is used in following transient **analysis**. In transient **analysis**, wave **propagation** in SAW sensor is investigated. Both analyses were performed using FEM code ANSYS.

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o numerically predict **crack** formation and growth **of** this model under accidental loading, it is necessary to characterize fracture properties at **the** microscopic level. To approach this objective a complete code **of** program using **finite** **element** method was written by **the** authors in MathCAD software. **The** geometrical characteristics, material properties and boundary conditions are attributed to **the** model. Corresponding **finite** **element** **analysis** was performed to determine **the** evolution **of** stress and strain states. For more comprehensible results and better facileness for comparison Von Misses stress had been calculated across **the** model using Eq. (1).

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In this paper, a systematic approach for elastic **finite** strain **crack** **propagation** with multiple cohesive cracks and self-contact is described. **Crack** paths are deter- mined by **the** CTOD method and **the** advance crite- rion uses either **the** equivalent stress intensity factor or **the** tip-**element** stress. **Crack** intersections, coales- cence and cohesive laws are accounted for, as is **the** for- mation **of** multiple particles. Globally-optimized mesh repositioning is used to minimize **the** least-square **of** all elements’ inner-angle error. This is followed, in a stag- gered form, by a Godunov-based advection step for **the** deformation gradient. Several examples are presented showing **the** robustness and accuracy **of** **the** implemen- tation, as well as **the** ability to represent **crack** face thickness variation in **finite** strains. Classical fracture benchmarks are solved and a problem **of** multiple **crack** evolution is proposed. Excellent results were observed in **the** effected tests.

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Abstract: Seals have wide application in automotive products. They are responsible for sealing **the** car in several parts such as **the** doors, **the** air intake cowl seal, and air intake lights seal. Strain and stress studies are very important in order to understand **the** behavior **of** polymeric **materials**, which are generally submitted to great workload variation and environmental influence. This study **of** EPDM rubber was carried out to define **the** strain, stress and yield stress. Tensile and compression tests were carried out on workpieces with 100 mm **of** length. **The** data were acquired using **the** Qmat software. A **Finite** **Element** **Analysis** using **the** MSC Marc Mentat™ was conducted and compared with experimental tests. **The** results showed an increase **of** effort proportional to bulb thickness. **The** proportional increase **of** compression effort for different displacements was significant. Moreover, physical parameters such as length, thickness, and friction coefficient changed **the** strain and stress rate.

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matrix with subsequent loading. With continuous increase in load, **crack** **propagation** occurred through successive adjacent regions **of** fibres and matrix. **The** longitudinal splits observed in **the** **propagation** zone were secondary fractures and they were developed after transverse **crack** **propagation**. This is established through study **of** hackle directions (directions are reversed) on similar split surfaces on either side **of** transverse fracture. After **the** **crack** propagated to certain distance, **the** net load carrying capacity **of** **the** composite reduced to that **of** **the** applied load resulting in an unstable fracture. **The** step in final fracture was a successive fracture and it was not related to bridging. **The** direction **of** hackles on a similar longitudinal split surface on mating fracture surface shows similar orientation. Therefore, longitudinal splitting is a primary fracture and it occurred before transverse fracture. Longitudinal fracture occurs when **the** shear stress, τm, in **the** matrix reaches **the** ultimate shear stress, τmu. Longitudinal splitting may occur either due to longitudinal fracture **of** matrix or debonding process. Since **the** aerospace grade composite has good interfacial strength, **the** debonding stress τd is greater than **the** ultimate shear stress **of** **the** matrix, τmu, Hence, in such composites, longitudinal fracture **of** matrix occurs in preference to Figure 10. Random fibre fracture directions indicated by white

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