scholarly journals A Numerical Approach for the Design of RC Beams Subjected to Axial and Transverse Loads

2021 ◽  
Vol 1203 (3) ◽  
pp. 032108
Author(s):  
Amal Wahbi ◽  
Duc Toan Pham ◽  
Ghazi Hassen ◽  
Denis Garnier ◽  
Patrick de Buhan
Keyword(s):  
Finite Element ◽  
Limit Analysis ◽  
Optimization Method ◽  
Numerical Approach ◽  
Rc Beams ◽  
Present Contribution ◽  
Transverse Loads ◽  
Numerical Predictions ◽  
Analysis Theory ◽  
Mixed Modelling

Abstract The present contribution deals with a numerical approach for the design of RC beams subjected to axial and transverse loads. It is based on the finite-element implementation of the kinematic approach of the yield design (or limit analysis) theory combined with a “mixed modelling” where the concrete material is regarded as a classical two-dimensional continuum while the longitudinal reinforcements are modelled as one-dimensional elements working in tension-compression only. For the beams reinforced in shear, stirrups are incorporated in the analysis through a homogenization procedure. An optimization problem is formulated, then solved using conic quadratic optimization method. As a result, an upper bound estimate to the yield strength domain of RC beams may be drawn in the plane of axial and transverse loads. For illustrative purpose, calculations are conducted on typical RC beams with different longitudinal and transverse reinforcement degrees. Furthermore, it is shown that such numerical predictions prove to be in good agreement with the results derived from other numerical simulations of the same problem using a finite element-based limit analysis commercial software. In order to assess their practical validity, these predictions are also compared to some available experimental results published in the literature.

Prediction of Microelectronic Substrate Warpage Using Homogenized Thermomechanical Finite Element Models

2005 ◽  
Author(s):  
Parsaoran Hutapea ◽  
Joachim L. Grenestedt ◽  
Mitul Modi ◽  
Michael Mello ◽  
Kristopher Frutschy
Keyword(s):  
Finite Element ◽  
Effective Properties ◽  
Isothermal Condition ◽  
Numerical Approach ◽  
Thermomechanical Properties ◽  
Temperature Changes ◽  
Numerical Predictions ◽  
Homogenization Approach ◽  
Simple Bounds ◽  
Complex Features

High-density microelectronic substrates, used in organic CPU packages, are comprised of several polymer, fiber-weave, and copper layers and are filled with a variety of complex features such as traces, micro-vias, Plated-Through-Holes (PTH), and adhesion holes. When subjected to temperature changes, these substrates may warp, driven by the mismatch in Coefficients of Thermal Expansion (CTE) of the constituent materials. This study focused on predicting substrate warpage in an isothermal condition. The numerical approach consisted of three major steps: estimating homogenized (effective) thermomechanical properties of the features; calculating effective properties of discretized layers using the effective properties of the features; and assembling the layers to create 2D Finite Element (FE) plate models and to calculate warpage of the whole substrates. The effective properties of the features were extracted from 3D unit cell FE models, and closed-form approximate expressions were developed using the numerical results, curve fitting, and some simple bounds. The numerical approach was applied to predict warpage of production substrates, analyzed, and validated against experimentally measured stiffness and CTEs. In this paper, the homogenization approach, numerical predictions, and experimental validation are discussed.

Analysis and Optimization of Metal to Composite Joints for Marine Structures

2014 ◽  
Vol 556-562 ◽  
pp. 91-95
Author(s):  
Xiao Wen Li ◽  
Ping Li ◽  
Zhuang Lin ◽  
Dong Mei Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mechanical Performance ◽  
Optimization Method ◽  
Additional Stress ◽  
Marine Structures ◽  
Hybrid Joint ◽  
Composite Joint ◽  
Numerical Predictions ◽  
Element Method

Composite to metal joints as important components of marine structures are gradually found in the marine industry. The purpose of this study is to investigate mechanical performance and optimization method of the composite sandwich to steel joints. The main emphasis was placed on the mechanical properties of a hybrid joint between a sandwich glass fibre reinforced plastic superstructure and a steel main hull. Based on the experiments of a base joint, a new finite element method was used to analyze a series of joints. The optimized joint was presented due to reducing weight and enhancing the mechanical performance. The numerical predictions of the base hybrid joint showed a very good correlation with the experiment results, which validated the reliability of the new finite element method. The strength of the optimized joint was also evaluated by finite element method. The result is similar to the base joint. And there is no additional stress concentration in weak parts. The optimized joint has 30% lower weight than the base joint, and the stress is only about 5% ~ 56% of the base one. The results of the present work imply that the change of geometric parameter is an effective method to improve the performance of the metal to composite joint.

Notched Specimens Fracture Prediction with an Advanced GTN Model

2011 ◽  
Vol 488-489 ◽  
pp. 77-80
Author(s):  
Joseph Fansi ◽  
Mohamed Ben Bettaieb ◽  
Tudor Balan ◽  
Xavier Lemoine ◽  
Anne Marie Habraken
Keyword(s):  
Dual Phase Steel ◽  
Damage Model ◽  
Numerical Approach ◽  
Void Coalescence ◽  
Present Contribution ◽  
Notched Specimens ◽  
Numerical Predictions ◽  
Growth Laws ◽  
Gtn Damage Model ◽  
User Material Subroutine

This present contribution consists of implementing an advanced GTN damage model as a "User Material subroutine" in the Abaqus FE code. This damage model is based on specific nucleation and growth laws in order to predict the void coalescence properties of the material. When applied, this implementation predicts the damage evolution and the stress state of notched specimens made from dual phase steel. By comparing numerical predictions with experimental results, the numerical approach was improved and then validated.

scholarly journals Application of an Advanced GTN Model

2012 ◽  
Author(s):  
Joseph Fansi ◽  
Anne-Marie Habraken ◽  
Tudor Balan ◽  
Xavier Lemoine ◽  
Caroline Landron ◽  
...  
Keyword(s):  
Dual Phase Steel ◽  
Damage Model ◽  
Numerical Approach ◽  
Present Contribution ◽  
Notched Specimens ◽  
Numerical Predictions ◽  
Growth Laws ◽  
Gtn Damage Model ◽  
User Material Subroutine ◽  
X Ray Absorption

The present contribution consists of implementing an advanced GTN damage model as a “User Material subroutine” in the Abaqus FE code. This damage model is based on specific nucleation and growth laws. This model is applied to the prediction of the damage evolution and the stress state in notched specimens made of dual phase steel. By comparing numerical predictions with experimental results based on high-resolution X-ray absorption tomography, the numerical approach was improved and validated.

Optimization Method of the Rubber Elastic Element Structure Based on the Vibrational Power Flow

2012 ◽  
Vol 605-607 ◽  
pp. 1244-1248
Author(s):  
Wen Wu Liu ◽  
Jing Jun Lou ◽  
Hai Ping Wu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Optimization ◽  
Elastic Element ◽  
Power Flow ◽  
Flow Analysis ◽  
Optimization Method ◽  
Analysis Theory ◽  
Vibration Power Flow ◽  
Vibrational Power Flow

The isolation design of the ship must be considered based on flexibility, usually using vibration power flow analysis theory. The proposed vibration power flow based on finite element method aims the optimization to minimize the vibration power flow. The rubber elastic element structural optimization method has been study as follows.

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