In this article, we apply the first elliptic function equation to find a new kind of solutions of nonlinear partial differential equations （PDEs） based on the ho- mogeneous balance method, the Jacobi elliptic expans...In this article, we apply the first elliptic function equation to find a new kind of solutions of nonlinear partial differential equations （PDEs） based on the ho- mogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method. New exact solutions to the Jacobi elliptic functions of a nonlinear PDE describing pulse narrowing nonlinear transmission lines are given with the aid of computer program, e.g. Maple or Mathematica. Based on Kirchhoff＇s current law and Kirchhoff＇s voltage law, the given nonlinear PDE has been derived and can be reduced to a nonlinear ordinary differential equation （ODE） using a simple transformation. The given method in this article is straightforward and concise, and can be applied to other nonlinear PDEs in mathematical physics. Further results may be obtained.展开更多
The elasticity-based Locally Exact Homogenization Theory(LEHT) is extended to study the mechanical-hygrothermal behaviors of unidirectionally-reinforced composites. Based on the framework developed previously, thermal...The elasticity-based Locally Exact Homogenization Theory(LEHT) is extended to study the mechanical-hygrothermal behaviors of unidirectionally-reinforced composites. Based on the framework developed previously, thermal and moisture effects are incorporated into the LEHT to study the homogenized and localized responses of heterogeneous materials, which are validated using available analytical and numerical techniques. The LEHT programs are then encapsulated as subroutines with Input/Output(I/O) interfaces, to be readily applied in different computational scenarios. In order to illustrate the efficiency of the LEHT, the theory is firstly coupled to the Particle Swarm Optimization(PSO) algorithm in order to minimize the axial thermal expansion mismatch in hexagonal and square fiber arrays by tailoring the fiber volume fraction. The LEHT is then implemented into the lamination theory to study fabrication-induced residual stresses arising during the cool-down process which introduces local laminate stresses owing to thermo-mechanical property mismatch between plies. Both of these applications illustrate the efficiency and accuracy of the LEHT in generating effective properties and local stress distributions, making the theory a golden standard in validating other analytical or numerical techniques as well as a reliable tool in composite design and practice for professionals and non-professionals alike.展开更多
文摘In this article, we apply the first elliptic function equation to find a new kind of solutions of nonlinear partial differential equations （PDEs） based on the ho- mogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method. New exact solutions to the Jacobi elliptic functions of a nonlinear PDE describing pulse narrowing nonlinear transmission lines are given with the aid of computer program, e.g. Maple or Mathematica. Based on Kirchhoff＇s current law and Kirchhoff＇s voltage law, the given nonlinear PDE has been derived and can be reduced to a nonlinear ordinary differential equation （ODE） using a simple transformation. The given method in this article is straightforward and concise, and can be applied to other nonlinear PDEs in mathematical physics. Further results may be obtained.
文摘The elasticity-based Locally Exact Homogenization Theory(LEHT) is extended to study the mechanical-hygrothermal behaviors of unidirectionally-reinforced composites. Based on the framework developed previously, thermal and moisture effects are incorporated into the LEHT to study the homogenized and localized responses of heterogeneous materials, which are validated using available analytical and numerical techniques. The LEHT programs are then encapsulated as subroutines with Input/Output(I/O) interfaces, to be readily applied in different computational scenarios. In order to illustrate the efficiency of the LEHT, the theory is firstly coupled to the Particle Swarm Optimization(PSO) algorithm in order to minimize the axial thermal expansion mismatch in hexagonal and square fiber arrays by tailoring the fiber volume fraction. The LEHT is then implemented into the lamination theory to study fabrication-induced residual stresses arising during the cool-down process which introduces local laminate stresses owing to thermo-mechanical property mismatch between plies. Both of these applications illustrate the efficiency and accuracy of the LEHT in generating effective properties and local stress distributions, making the theory a golden standard in validating other analytical or numerical techniques as well as a reliable tool in composite design and practice for professionals and non-professionals alike.
