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A series of luminescence phosphors M0.955Al2 –xGaxSi2O8∶Eu2+ (M=Ca, Sr, Ba, x = 0~1.0) were prepared via solid-state reaction in weak reductive atmosphere. The lattice positions were discussed. It was found that when Ga3+ entered MAl2Si2O8 lattice and substituted Al3+, complete solid solutions formed. The lattice parameters (a, b, c) and unit cell volume of phosphors M 0.955Al2 –xGaxSi2O8: Eu2+ (M=Ca, Sr, Ba, x = 0~1.0) increased linearly, the lattice parameters (α, β,γ) of Ca0.955Al2–xGaxSi2O8∶Eu2+(CAS) decreased linearly and the lattice parameter β of Sr0.955Al2–xGaxSi2O8∶Eu2+(SAS) and Ba0.955Al2–xGaxSi2O8∶Eu2+(BAS) increased linearly as Ga3+ content increased.

For the purpose of construction an effective element model, the US- FE-LSPIM TRI3 element formulation, which is based on the concept of unsymmetric finite element formulation, is established. Classical linear triangle shape functions and FE-LSPIM TRI3 element shape functions are used as test and trial functions respectively. Classical linear triangle shape functions fulfill the requirements of continuity in displacement field for test functions. The FE-LSPIM TRI3 element shape functions synthesize the individual strengths of meshfree and finite element methods so they are more proper for trial functions. The element is applied in free vibration analysis of two dimension solids. Typical benchmark problems are solved. The results show that this element is more accurate and capable of good performances under both regular and irregular meshes.

A new formulation of triangle element is developed. Based on the concept of unsymmetric finite element formulation, classical linear triangle shape functions are used as test functions, and FE-LSPIM TRI3 element shape functions are used as trial functions. The former is fulfill the requirements of intra-element and inter-element continuity in displacement field, and the latter is a good alternative for requirements of completeness in displacement field. Typical test problems for static solids are analyzed. The results show that the proposed element has good accuracy, and is superior to classical linear triangle element and isoparametric quad element.

This US-FE-LSPIM QUAD4 element is formed by using two different sets of shape functions for the trial and test functions, viz. sets of FE-LSPIM QUAD4 element shape functions and sets of classical isoparametric shape functions. For some test problems, the US-FE-LSPIM QUAD4 element has good accuracy. And by compared with FE-LSPIM QUAD4 element, the proposed element does not need to use Penalty method or Lagrange multiplier method to ensure fulfilment of exact essential boundary condition along the entire length of the edge. This paper further studies the performance of US-FE-LSPIM QUAD4 element on mesh distortion. Numerical test examples show that the element exhibits high precisions even under the mesh distortions. The US-FE-LSPIM QUAD4 element displays good tolerance to the mesh distortions