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A SIMPLE UNIFIED SET OF DISPLACEMENT AND VELOCITY APPROXIMATIONS IS PRESENTED TO EXPRESS VARIOUS TWO-STAGE COMPOSITE TIME INTEGRATION SCHEMES. BASED ON THE UNIFIED APPROXIMATIONS, TWO NOVEL SETS OF OPTIMIZED PARAMETERS ARE NEWLY PROPOSED FOR THE IMPLICIT COMPOSITE SCHEMES TO ENHANCE THE CAPABILITY OF CONSERVING TOTAL ENERGY. TWO SPECIAL CASES OF THE UNIFIED APPROXIMATIONS ARE ALSO CONSIDERED TO OVERCOME SOME SHORTCOMINGS OF THE EXISTING SCHEMES. BESIDES, THE NEWLY PROPOSED UNIFIED SET OF APPROXIMATIONS CAN INCLUDE MANY OF THE EXISTING COMPOSITE TIME INTEGRATION SCHEMES. TO BE SPECIFIC, BOTH IMPLICIT AND EXPLICIT COMPOSITE SCHEMES CAN BE EXPRESSED BY USING THE UNIFIED SET OF APPROXIMATIONS. THUS, BOTH IMPLICIT AND EXPLICIT TYPES OF COMPOSITE SCHEMES CAN BE SELECTED FROM THE UNIFIED SET BY SIMPLY CHANGING ALGORITHMIC PARAMETERS. TO DEMONSTRATE ADVANTAGEOUS FEATURES OF THE PROPOSED UNIFIED SET OF APPROXIMATIONS, VARIOUS NUMERICAL EXAMPLES ARE SOLVED AND RESULTS ARE ANALYZED.
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