Hi,
Yes, looking at the bulb as a resistor the resistance of a 115vac, 115 watt bulb would be 115 ohms. At 230vac it would consume 4 times that power if it could survive which would be 460 watts. Half that is 230 watts, still too much. We actually need 1/4 of that not 1/2.
Solving for the RMS voltage with time, then solving for the time to produce 115 watts, we find that it would take a firing angle of 90 degrees but for only one half cycle (as with an SCR). With a triac firing every half cycle we'd need to fire at 113.827 degrees and 180+113.827 degrees. That would give us two partial sines of width about 66.173 degrees each.
The total average power with either of these would be 115 watts at 230vac.
The peak of this second scheme would be a max of about 297.5v so it would be much higher than the normal peak of 170v for a 120vac line, but the peak would not last as long.
The peak of the 90 degree scheme would be just as high as the line voltage peak which is 230*1.4142=325 volts, pretty high for a 170v max bulb, and the peak would last just as long as the normal operating peak.
The average heating power would be the same now but I've never tried this myself. If the filament mass is not enough to properly integrate the voltage peaks, it could see a temporary but repetitive rise in temperature that exceeds it's normal rating and thus limit the life to less than normal. Average power heating is one thing, but instantaneous power could cause instantaneous rises in temperature which although average out to the normal working temperature could be far above that for short time periods.
There was a bulb model around on the web a few years back. The time constant of the filament would be the important thing.
We see unusual side effects with LED's too when they are driven with pulses instead of a constant level. Sometimes the color changes a little bit simply because the peak current is not at the normal level.