For a more intense smile:
* Beamed
* Grinned
* Chortled (suggests a hearty, playful laugh)
* Guffawed (suggests loud laughter)
* Cackled (suggests a harsh, shrill laugh)
For a more subtle or enigmatic smile:
* Smirked (suggests knowingness or amusement)
* Glimmered (suggests a faint, but hopeful smile)
* Twinkled (suggests a playful or mischievous smile)
* Flashed (suggests a quick, bright smile)
For a more formal or polite smile:
* Graced (suggests a dignified smile)
* Courted (suggests a flirtatious smile)
* Illuminated (suggests a radiant smile)
Ultimately, the best "strong" verb will depend on the specific situation and the effect you want to achieve.