Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, ani...Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.展开更多
Sandwich materials are widely used in marine structures because of their excellent comprehensive properties.However,the solution of bimodulus is challenging.Therefore,the theoretical and numerical approximation method...Sandwich materials are widely used in marine structures because of their excellent comprehensive properties.However,the solution of bimodulus is challenging.Therefore,the theoretical and numerical approximation methods for the analysis of load-bearing characteristics of bimodulus sandwich structures are put forward comprehensively in this paper.Based on the superposition principle,a theoretical method for calculating the neutral surface position of bimodulus sandwich plate is derived,and the corresponding bending control equation is obtained.The proposed theoretical approximation method can fully consider the sawtooth deformation between the plate and the core,as well as the sawtooth deformation inside the core at the tension–compression interface.Moreover,a finite element model is established for complex sandwich structures to analyze the influence of bimodulus.Numerical examples show that the theoretical approximation model proposed in this paper has higher calculation accuracy.展开更多
The serious warpage issues of ultrathin chip-on-flex(UTCOF) assembly induced by mismatched thermal stresses have greatly affected the mechanical stability and reliability of emerging ultrathin chip packaging technolog...The serious warpage issues of ultrathin chip-on-flex(UTCOF) assembly induced by mismatched thermal stresses have greatly affected the mechanical stability and reliability of emerging ultrathin chip packaging technology. Currently, a theoretical prediction as a convenient and straightforward approach is still lacked for describing effectively the thermal-mechanical behavior of UTCOF during the adhesive curing and cooling process. In consideration of the adhesive thickness approximating to ultrathin chip and flexible substrate thickness, we develop a layerwise-model of ultrathin chip-adhesive-flex structure under plain strain condition, where the behavior of thick adhesive bonding can be described precisely through increasing the subdivided mathematical plies. Further, the analytical results show that the concave and convex forms of ultrathin chip warpage yield at the end of the curing and cooling process respectively. Meanwhile, the effects of its structure dimensions and material properties are also revealed for discussing a way to relieve the extent of ultrathin chip warpage. Additionally, in order to verify the validity of the theoretical prediction, we also introduce the corresponding numerical technique and experimental method. These results suggest that a kind of rigid and ultrathin flexible substrate such as metal foil should be adopted for small warpage of ultrathin assembly.展开更多
文摘Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.
基金supported by the National Natural Science Foundation of China(51979213).
文摘Sandwich materials are widely used in marine structures because of their excellent comprehensive properties.However,the solution of bimodulus is challenging.Therefore,the theoretical and numerical approximation methods for the analysis of load-bearing characteristics of bimodulus sandwich structures are put forward comprehensively in this paper.Based on the superposition principle,a theoretical method for calculating the neutral surface position of bimodulus sandwich plate is derived,and the corresponding bending control equation is obtained.The proposed theoretical approximation method can fully consider the sawtooth deformation between the plate and the core,as well as the sawtooth deformation inside the core at the tension–compression interface.Moreover,a finite element model is established for complex sandwich structures to analyze the influence of bimodulus.Numerical examples show that the theoretical approximation model proposed in this paper has higher calculation accuracy.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51475195, 51322507 & 91323303)National Science and Technology Support Program (Gant No. 2015BAF11B02)
文摘The serious warpage issues of ultrathin chip-on-flex(UTCOF) assembly induced by mismatched thermal stresses have greatly affected the mechanical stability and reliability of emerging ultrathin chip packaging technology. Currently, a theoretical prediction as a convenient and straightforward approach is still lacked for describing effectively the thermal-mechanical behavior of UTCOF during the adhesive curing and cooling process. In consideration of the adhesive thickness approximating to ultrathin chip and flexible substrate thickness, we develop a layerwise-model of ultrathin chip-adhesive-flex structure under plain strain condition, where the behavior of thick adhesive bonding can be described precisely through increasing the subdivided mathematical plies. Further, the analytical results show that the concave and convex forms of ultrathin chip warpage yield at the end of the curing and cooling process respectively. Meanwhile, the effects of its structure dimensions and material properties are also revealed for discussing a way to relieve the extent of ultrathin chip warpage. Additionally, in order to verify the validity of the theoretical prediction, we also introduce the corresponding numerical technique and experimental method. These results suggest that a kind of rigid and ultrathin flexible substrate such as metal foil should be adopted for small warpage of ultrathin assembly.
